Joan Regent? No way. Also, why would she escape captivity?
Come now, a regent who can't read nor write wouldn't be
that much worse than some presidents we have today.
But, jokes aside, Jeanne isn't going to be regent. Most likely candidates for that are either the king's mother (Marie d'Anjou), or more technically, his grandmother, Yolande of Aragon; or the senior most prince du sang, let's look at who's available:
Charles, duc d'Orléans is the most senior royal male. But unfortunately, he's been captive in England since the 1410s. So even
if he gets boots on the ground in France, he might/will be distrusted by the French. Also, there's this whole rivalry between the Armagnacs (his wife's family) and the Burgundian Valois. England might decide to release him to cause chaos in France, but I can't be sure.
Next batter up is Jean, Comte d'Angoulême, younger brother to Orléans. I can't find much on him in the way of political views or affiliations, he might go
with his brother's anti-Burgundian policy, he might go
against it, depending on a lot of things. Also, he's still single, so whoever's going to look at wedding him to one of their daughters to maximise the hold they have on him if he's no more than a straw man.
The duc d'Anjou, brother of Queen Marie. Louis was more interested in conquering Naples than France,
but him being forced to stay in France might butterfly his death from malaria, and a POD in 1430 might change who he's married to. OTL he was betrothed to a daughter of the duke of Burgundy (the OTL duchess of Bedford, I think), but the plan for a marriage between the Anjous and the Burgundians fell by the wayside at the murder of the duke. His sister was engaged to the duke of Brabant though (she later married the duke of Brittany), so I'm sure the duke of Burgundy (if it were in his interest) can scrape up some pretty little niece or cousin to marry.
The duke of Lorraine, brother of Queen Marie and the duc d'Anjou. Le Bon Roi René is still only
jure uxoris duke of Lorraine at this point, but if, by some miracle, all three ahead of him aren't available, the regency is his. (Personally, I feel the chances that we're going to see an Angevin/Yolande of Aragon dominated regency, are pretty strong). René seems (from what I remember) to have been a fair politician, and his wife was a reasonably smart tack, since she often served as regent in Anjou in René's absences.
The comte du Maine. Youngest brother of Anjou, Lorraine and Queen Marie. Don't know much about him, so can't comment. Like Angoulême and Anjou he's still unmarried, so someone might be interested in achieving power through a marriage of his daughter to Maine. I would warn that after this, the princes du sang listed are moving into rather ASB territory, since I'm mentioning them for the sake of completeness, rather than the likelihood of them being regent.
The duke of Burgundy. OTL, in two years from the POD, the Anglo-Burgundian alliance was fraying. And Burgundy was, while opposed to the mainline Valois in theory, didn't simply wish to set up a Plantagenet king in their place. They wanted France weaker, not conquered. He has reasonably powerful connections through his sisters - the duchesses of Brittany, Cleves, Bedford and Bourbon - so he might still be a mover and shaker in France
if things look like they're leaning too far against him. Philippe was a wily old dog who knew how to work the political street, so it's not unthinkable.
The duke of Brabant. Betrothed to the youngest sister of the duke of Anjou. His cousin, Burgundy, might use him in the event that we see an Angevin-dominated regency, as a way of connecting Burgundy to the side of the government. Unfortunately, Brabant was dead before the year was out.
The comte de Nevers. Cousin of Burgundy, unwed, don't know about his political opinions.
The duc d'Alençon. Son-in-law of the duc d'Orléans. Might be included on the regency council due to him being closely related (by marriage, if not blood, which is a lot more distant) to the new king. His wife is the king's paternal cousin. But at the same time, Alençon was later executed for treason by Louis XI, and his future second wife is an Armagnac.
Basically, IMHO we're going to see an Angevin dominated regency, that's going to have to walk a tightrope between the Armagnac and Burgundian factions if they want to pull France
out of the mess it's in. England's struggling, but the coup de grace hasn't been dealt yet, so it's not down, and it's not out. The duke of Bedford's sitting in Paris, and his wife's OTL death is still two years in the future. His wife's death was what led to the breaking of the Anglo-Burgundian alliance OTL. Here, that might be different. The duchess may live, or Burgundy may decide to jump from the English ship if France offers him good enough terms.