The House of Valois-Orleáns is basically neutralized, as the remaining sons, Charles and Jean of the only other brother of Charles VI, Louis of Orleáns, are in English captivity by 1415. One would have to trace descent all the way back to the second son of Jean II, Louis I, Duke of Anjou, which in turn goes down to his son Louis II, who died in 1417, and was succeeded by his oldest son Louis III, who would now be the next dynast if the Orleáns line is unavailable. Most importantly, Louis III's mother is Yolande of Aragon, and if she fought hard for her OTL son-in-law Charles VII, she would especially go hard for her own son. Louis of Anjou would be in Naples trying to secure that succession for himself, but this new situation probably sees him summoned to his mother's side immediately.
Gaining allies would be the first order of business for Louis and Yolande and the at this point 19 year old Louis is undoubtedly getting married. What if Yolande was able to bring Philip the Good to the negotiating table and manages to convince him to switch sides? Philip may not have daughters, but he does have unmarried sisters in 1422, the widowed, but older Margaret, and both the younger Anne and Agnes, of whom Anne was married to John of Bedford in OTL to secure the Anglo-Burgundian alliance. It would be contentious, but the Orleáns brothers have scant support while they're in captivity and likely have to see themselves pragmatically skipped in the succession from behind bars.
The English could struggle with an Anjou-Burgundy alliance if they can't convince more French nobles to back their infant king's claim, many of whom may decide to back Louis of Anjou. Catherine of Valois is in England. Dwindling support may see the English prudently decide to come to the negotiating table and hammer out a peace agreement vacating the infant's claim, recognizing Louis of Anjou as Louis XI of the House of Anjou and perhaps making a betrothal between Henry and a future daughter of Louis and Anne/Agnes, but at the same time securing English possessions like Calais and Gascony.
Now having pulled out of France, the English can focus fully on the regency government and may possibly even avert the Wars of the Roses, which were in part fueled by English defeat in France over the years. TTL Louis XI could decide to bequeath his own claims to Naples and Sicily to his brother René or continue to pursue them himself, once he's finished consolidating his power in France. Philip makes a different 2nd marriage than he did in OTL and might butterfly away Charles the Bold.
) he won't want his cousins to be released.