Here is my very long POD for a successful New France. I tried to use as many primary documents as possible instead of relying on secondary sources including newspapers, treaties, censuses and other documents that I found at my university library. I tried to avoid using basic textbooks or the internet as authoritative sources (especially wikipedia which is not a good source for history). I'll be posting this in seperate parts since it is long.
EARLY HISTORY
In 1541 when Cartier was on his third trip to the New World he was not as warmly greeted by the Iroqouis as he had been on his previous voyages. He had ruined relations with the local Iroquois by kidnapping their chief Donnacona and taking him and his sons back to France on his second voyage. This led to a winter where Cartier's group of 300 men was constantly under siege by the Iroquois. Meanwhile, the Francis I had sent five ships carrying hundreds of colonists under the command of Jean-François de la Rocquer de Roberval to meet up with Cartier in 1542 and set up the first colony at Charlesbourg Royal (outside of Quebec). However, Cartier abandoned them and returned to France instead, and the colony failed basically having to abandon the New World. This stalled French settlement for another century.
So what if the settlement had not failed because Cartier had not kidnapped Donnacona? Instead Cartier guided the settlers and stayed behind with his men. The settlement was to have over 1,000 people including men and women. This settlement would have led to the French establishing other colonies including one on Île Saint-Jean (Prince Edward Island), where the French had noted that there were plentiful birds to be eaten and the land was very fertile making it an optimal place for colonisation. A colony could have been founded here by Breton and Basques, who already spent half of their year fishing cod in the grand banks south of Newfoundland. By 1600 I estimate that there can be around 15,000 French in settlements along the St. Lawrence River and in the Maritimes as well as Newfoundland, in addition there will probably be another few thousand Métis and an equal number of converted Iroquois under French protection. I arrived at this number by estimating the rate of natural increase of the French in America in the mid-17th century (much higher than in France) and by adding on average 100 permanent settlers each year.
At the dawn of the 17th century, the French in OTL established settlements in Acadia, including one in Sainte-Croix (Maine) and at Port Royal in Acadia in 1604/1605. Initially I estimate these areas will be settled earlier with perhaps 1,000 colonists and they will increase with contact with the already established areas along the St. Lawrence making them much more viable than they were in the beginning. Not having been as isolated as they were settlement will proceed faster. So by 1630 there are about 45,000 French in North America. In this TL I have the French having more contact with the Iroquois and therefore using boiled white birch leaves as a cure for scurvy. Cartier learned of this but left too early so in this TL he stays on to guide Robertval's group and this becomes a common cure reducing the death rate of early colonists.
After 1620 there was a huge demand for beaver pelts in Europe will bring the population to increase with many men seeking fortune going to New France. In OTL many Frenchmen arrived in New France but did not stay since after 1632 the French Crown prohibited the establishment of new seigneuries west of the Montréal. The reason being that the settlements were minuscule and white settlement could not be pushed further west and south since they crown did not want to have to defend all of these settlers. Instead the crown pushed for European-village style settlements, but these proved unpopular in this where despite the dangers settlers preferred large farms with detached homes. So, with a population of 40,000 instead of 400 the crown will probably keep granting seigneuries since the colonists can readilly defend themselves. This was actually the plan of Intendant Jean Talon at the time. So with the increase in the demand for beaver pelts the French would have already be as far south as Detroit by 1650. However, slowly hunting grounds will be taken over by agriculture, pushing hunting further south and basically this will be a cycle.
With the arrival of the English and Dutch in North America, Cardinal Richelieu and Louis XIV (at least in the early part of his reign) did in OTL take an interest in the North American colonies and wanted them to grow. This led to the formation of the Compagnie des Cent-Associés. This company was granted a monopoly on trade and had to pay for the passage of 160 settlers every year for twenty-five years. In this TL I have this company being entrusted with the great lakes region instead of the St. Lawrence valley since that area is already settled. In OTL it was hard to get many French offciers to stay in this area permanently because the seigneuries dried up and the poor climate and native attacks greatly hurt the reputation of the colony. However, by this time New France is not as remote or unsafe as it was in OTL. Plus with the fertile lands of modern Michigan and Southern Ontario they have more incentive to stay. Also land is being given to the coureurs des bois whom in OTL were not allowed to settle these areas permanently even though many petitioned the crown do be able to. In OTL 2/3 of them returned to France. Here they would have been likely to remain on the land. Also with Louis XIV having created the Filles du Roi, where young women had their passage sponsored to America, I estimate the European population would have reached 120,000 by 1680. Again this takes into account not much more net immigration than New France, but is based on most of the soldiers and coureurs des bois remaining in the Americas and a few more immigrating. This population growth is mostly based on natural increase. By that time Acadia has around 25,000 settlers and they are living much the way the Acadians lived using European-style village settlements instead of large seigneuries as in Canada. By the time of the Treaty of Utrecht in 1713 there would have been over 50,000 French in Acadie, again taking into account the high birthrate of the time. So instead of the British taking Acadia, in this TL they simply acquire a bit of Maine, Newfoundland and have their settlements on Hudson Bay returned.
EARLY HISTORY
In 1541 when Cartier was on his third trip to the New World he was not as warmly greeted by the Iroqouis as he had been on his previous voyages. He had ruined relations with the local Iroquois by kidnapping their chief Donnacona and taking him and his sons back to France on his second voyage. This led to a winter where Cartier's group of 300 men was constantly under siege by the Iroquois. Meanwhile, the Francis I had sent five ships carrying hundreds of colonists under the command of Jean-François de la Rocquer de Roberval to meet up with Cartier in 1542 and set up the first colony at Charlesbourg Royal (outside of Quebec). However, Cartier abandoned them and returned to France instead, and the colony failed basically having to abandon the New World. This stalled French settlement for another century.
So what if the settlement had not failed because Cartier had not kidnapped Donnacona? Instead Cartier guided the settlers and stayed behind with his men. The settlement was to have over 1,000 people including men and women. This settlement would have led to the French establishing other colonies including one on Île Saint-Jean (Prince Edward Island), where the French had noted that there were plentiful birds to be eaten and the land was very fertile making it an optimal place for colonisation. A colony could have been founded here by Breton and Basques, who already spent half of their year fishing cod in the grand banks south of Newfoundland. By 1600 I estimate that there can be around 15,000 French in settlements along the St. Lawrence River and in the Maritimes as well as Newfoundland, in addition there will probably be another few thousand Métis and an equal number of converted Iroquois under French protection. I arrived at this number by estimating the rate of natural increase of the French in America in the mid-17th century (much higher than in France) and by adding on average 100 permanent settlers each year.
At the dawn of the 17th century, the French in OTL established settlements in Acadia, including one in Sainte-Croix (Maine) and at Port Royal in Acadia in 1604/1605. Initially I estimate these areas will be settled earlier with perhaps 1,000 colonists and they will increase with contact with the already established areas along the St. Lawrence making them much more viable than they were in the beginning. Not having been as isolated as they were settlement will proceed faster. So by 1630 there are about 45,000 French in North America. In this TL I have the French having more contact with the Iroquois and therefore using boiled white birch leaves as a cure for scurvy. Cartier learned of this but left too early so in this TL he stays on to guide Robertval's group and this becomes a common cure reducing the death rate of early colonists.
After 1620 there was a huge demand for beaver pelts in Europe will bring the population to increase with many men seeking fortune going to New France. In OTL many Frenchmen arrived in New France but did not stay since after 1632 the French Crown prohibited the establishment of new seigneuries west of the Montréal. The reason being that the settlements were minuscule and white settlement could not be pushed further west and south since they crown did not want to have to defend all of these settlers. Instead the crown pushed for European-village style settlements, but these proved unpopular in this where despite the dangers settlers preferred large farms with detached homes. So, with a population of 40,000 instead of 400 the crown will probably keep granting seigneuries since the colonists can readilly defend themselves. This was actually the plan of Intendant Jean Talon at the time. So with the increase in the demand for beaver pelts the French would have already be as far south as Detroit by 1650. However, slowly hunting grounds will be taken over by agriculture, pushing hunting further south and basically this will be a cycle.
With the arrival of the English and Dutch in North America, Cardinal Richelieu and Louis XIV (at least in the early part of his reign) did in OTL take an interest in the North American colonies and wanted them to grow. This led to the formation of the Compagnie des Cent-Associés. This company was granted a monopoly on trade and had to pay for the passage of 160 settlers every year for twenty-five years. In this TL I have this company being entrusted with the great lakes region instead of the St. Lawrence valley since that area is already settled. In OTL it was hard to get many French offciers to stay in this area permanently because the seigneuries dried up and the poor climate and native attacks greatly hurt the reputation of the colony. However, by this time New France is not as remote or unsafe as it was in OTL. Plus with the fertile lands of modern Michigan and Southern Ontario they have more incentive to stay. Also land is being given to the coureurs des bois whom in OTL were not allowed to settle these areas permanently even though many petitioned the crown do be able to. In OTL 2/3 of them returned to France. Here they would have been likely to remain on the land. Also with Louis XIV having created the Filles du Roi, where young women had their passage sponsored to America, I estimate the European population would have reached 120,000 by 1680. Again this takes into account not much more net immigration than New France, but is based on most of the soldiers and coureurs des bois remaining in the Americas and a few more immigrating. This population growth is mostly based on natural increase. By that time Acadia has around 25,000 settlers and they are living much the way the Acadians lived using European-style village settlements instead of large seigneuries as in Canada. By the time of the Treaty of Utrecht in 1713 there would have been over 50,000 French in Acadie, again taking into account the high birthrate of the time. So instead of the British taking Acadia, in this TL they simply acquire a bit of Maine, Newfoundland and have their settlements on Hudson Bay returned.