Not only are you starting colonization earlier, but you're havingFAR more settlers come over than ever came iOTL. France had a terrible, terrible time getting people to settle New France, and wound shipping out prostitutes from prisons, because so very few respectable women would go.,
the founding population of Quebec, iotl, was effectively like 2.5k people.
And you havent explained why ten times as many people are willing to move. You have as many moving in single waves as ever settlled Quebec.
Why, too, would the government support such a very expensive proposition? Because it would be expensive.
In OTL 30,000 French set out for French North America between 1542 and 1760, of those only 27,000 survived the voyage and roughly 14,000 remained.
In my TL only 55,650 French arrive in America before 1700, and I did take into account return migration when calculating population growth, hence around 1/2 made it back to France. Also, I studied the early death rates to account for lower growth during the early years (due to scurvy, Indian attacks etc). Also, I did take into account intermarriage between French men and Indian women.
With earlier colonization, albeit in small numbers the population can grow much like similar "frontier societies". I studied Portuguese colonization of the Azores and Madeira, along with Dutch colonization of South Africa and English colonization of New England. I wanted to look at patterns in migration, death rates, infant mortality, disease, fertility, etc.
Some common occurrences are found in frontier societies. Firstly, unlike in Europe at the time people tend to live spread out rather than in villages. This greatly reduces the spread of disease and helps keep death rates down. Food is usually abundant due to the abundance of land, hence there being little risk of famine early on. Finally, marriage age is a lot younger than in Europe. In these societies, women were getting married much earlier and dowries were not as important due to the availability of land. Also, women tended to have far more children than their contemporaries in Europe because of the larger land holdings requiring more children.
Looking at "frontier regions" firstly the Azores, discovered by the Portuguese in the early 15th century. These islands were colonized by fewer than 4,000 settlers from both Portugal and Flanders. This occurred mainly between 1450-1480. By 1580 the population had risen to around 60,000 and one has to remember that there were thousands of deaths due to outbreaks of the plague along with natural disasters such as volcanoes and earthquakes. In addition, by 1541 the archipelago was so overpopulated that emigration to Brazil had begun and by 1580 an estimated 6,000 Azoreans had made it to Brazil. The Azores provided no cash crops, but they offered open land and the Portuguese crown decided to settle the islands. By the 1520s however the islands themselves were overcrowded and the villages began to resemble the places in mainland Europe where disease could easily spread.
Dutch South Africa too only received a net of 2,044 settlers between 1657 and 1806. By 1806, their descendants numbered 26,720. Even here there were outbreaks of smallpox in 1713 and 1755 killing 7% and 12.7% of the colonists. A century later their population would number just under 1 million.
So after 60 years of colonisation the French population numbers just under 23,000, which does not seem far fetched considering a net of around 4,000 French immigrants arrive during that period. However, outbreaks of disease (including small pox) and a slightly higher mortality do take their toll on the colonists.
During the 1600-1650 period a net of 16,000 settle, encouraged by the French government as by this period New France can be exporting grain to France albeit in small quantities. This would be comparable to New France during the 1700-1760 period when 40% of its immigrants arrived, albeit more attractive with less threats from the English.
During the 1650-1680 period another 9,000 settle permanently in New France. This is mostly encouraged by the French government to counter the English. After this period I have factored a net of around 200 new settlers per year, including around 1,000 prisoners from the English colonies who have been absorbed into the population (around the same number as in OTL).
As for the costs, France was far wealthier and larger than Portugal or the Netherlands, so to think the French crown couldn't bear the cost to send some people to the New World is ludicrous. Like any other power, the incentive would be to control more territory and hope to find wealth there. In the meantime, they are preventing other powers from acquiring said territory.
As for the composition of the immigrants, around 1/3 are indentured servants who are meant to be farmers, but early on many turn to the fur trade. They are recruited individually and in small groups by merchants. Their passage would be paid by merchants and often seigneurs to whom land was granted. Their rate of return would be rather high, especially early on.
The second group is military men, though smaller in number they are granted large tracts of land with the incentive to settle and farm. As in OTL, a larger number of these remained in New France and many would become seigneurs in their own right.
The "filles du roi" and other undesirable women mostly from Paris. By paying their passage, the French crown has a useful outlet for orphan girls along with undesirable women. For the women and girls, the new world offers an escape from stigma and a new beginning.
Clergy also form an important part of the migration. The Jesuits and other religious orders are given land grants and have a mission to convert the indigenous peoples of New France to the Catholic Church. Receiving support from the crown and the Church, this group would be perhaps 5% of all settlers during the 16th and 17th centuries.
There are also convicts. In OTL the French government sent men accused of petty crimes such as stealing and illegal poaching to the New World. Again, this is mutually beneficial for the France along with the colonies. It offers the opportunity to rid France of an undesirable element and offers the criminals a new beginning. Related to this group are disgraced upper class men, often libertines who can start a new beginning in the New World. Also, since seigneuries are purchasable, it money can buy a certain respectability in New France that it can't in France.
Another group that seems to come are skilled craftsmen. In New France the need for carpenters, stone masons, etc was so great that an apprentice could become a tradesman faster than in France. In OTL this was the primary group of settlers that arrived between 1714-1754. In fact 90% of the the skilled craftsman during this period were apprentices or peasants engaged in handicraft.
Finally there were settlers who arrived of their own volition. Perhaps 10% of the total, these tended to be adventurers and people who wanted land. Since New France has expanded beyond the Saint Lawrence River valley, there is an abundance of good farmland available to those willing to take the risk.
