John II of France not captured

in 1356 Edward, the Prince of Wales, the Black Prince led the English to victory at the Battle of Poitiers.
The King of France, John II was captured and held in captivity for four years.
Suppose John II of France is not captured.
The English are still victorious at the Battle of Poitiers. What happens then?

It would make the battle looking even more as a second Crécy (basically Jean II had the opportunity to flee, he just didn't), meaning it would probably limit the political damages.

Charles the Bad of Navarre would have an harder time creating havoc in France and that would lead to probably shorter negociations with England.
Instead of the OTL Treaty of London, you'd have something closer to the Treaty of Brétigny (or possibly, but it would ask for convenient events, less important than Brétigny)
Meaning no riots in Paris, lesser Jacquerie and more stable late reign of Jean II and earlier reign of Charles V. Basically, Caroline phase of the HYW goes even better for France.

Eventually, not that much change, except you get rid earlier of the crisis of late 50's and early 60's that Charles V resolved IOTL well enough for that it didn't have important effects (if something, showing early his skills).

Most consequences would affect the War of Succession of Brittany, where montfortistes may have an harder time winning the day.

This might be a bit random, but it might butterfly the formation of the Duchy of Burgundy as it came to be known. John II of France ended up bestowing the Duchy of Burgundy on his youngest son Philip and made him premiere peer of France for his bravery during the battle of Poitiers. Father and son were both captured together. The son apparently protected his father with a lot of valour. Those territories formed the basis which Philip's successors used to become formidable rivals to Kings of France. If not for Poitiers, it wouldn't be surprising if the youngest son got something else and Burgundy is given to someone else.

It should be noted that Philippe le Hardi didn't recieved Burgundy after the battle, but the apanage of Touraine in 1360, and eventually some sort of regency of Burgundy as "lieutenant-général" then the whole duchy.

Giving the OP, tough, it's more than probable that Philippe le Hardi would manage to avoid capture as Jean did ITTL, and maybe he wouldn't recieve Touraine.

Regarding Burgundy proper, the deep crisis the duchy knew a really important succession crisis in early 60's while the Capetian line of Burgundy ended (which itself could be butterflied, while not easily). Eventually someone had to rule the land to prevent it falling in even more disorder : Charles the Bad being out of question, he eventually let one of his sons to deal with.

Admittedly, it didn't have to be Philippe, but he was the most likely candidate being the only one not yet landed (especially if ITTL he doesn't recieve Touraine) and the other having too strategical holdings that they would be easily removed (Louis in Anjou, Jean in Berry).

Now that's good thinking there, but for not sceding Burgundy to Philippe, you may need a sub-PoD.