I just went over this TL and it's very interesting, but I've still not ended reading it.
My attention was caught by the longer lasting Hundred Years War, a topic especially more interesting for me as I just ended a book on that war by Georges Minois.
The major differences I've seen as of now is that Henry V lives longer and that Charles VII is somewhat victim of depression and unable to launch a reconquest.
Although Charles VII depression may delay a reconquest, I don't think that Henry V survival would be decisive and ITTL, even the attempt to take Bourges has failed. The main point for England would a less contested royal government in absence of a regency for Henri VI. But that doesn't change the strategic cards in France much.
As of France, I don't know if Yolande of Aragon is still there. Her role in reforming the court and putting competent men in important offices was essential in preparing the reconquest.
Also, there is Arthur of Richemont, brother of Jean V of Brittany, an able and competent military leader. Yolande of Aragon was one of his most important backers, but even if she is removed from the scene ITTL, that doesn't exclude he takes advantage of the depression of Charles VII to stage a coup, kind of reverse Praguerie.
The coup by the House of Foix seems a bit unlikely. I may conceive the feud between Armagnac and Foix resuming, but deposition? Since the capture of Paris by Burgundians, with the capture and execution of Bertrand d'Armagnac, the Armagnac faction had more or less been taken over by the Dauphin Charles. At worst, I would imagine Foix again switching sides and defecting to England.
But anyway, deposing Charles VII and his son, that would be opening the door to the newt guy on the line of succession to the throne, who is none other than Philip the Good, Duke of Burgundy, since Charles of Orleans is dead.
His alliance with Henry V was more one of opportunity and the ambitious Burgundians waited the first occasion to renegade their alliance, like John Fearless tried at Montereau, and like his son did at Arras. Removing Charles VII from the scene is removing a major obstacle to such an alliance, and removing his son is more or less an invitation for the Duke of Burgundy to sit on the throne, one thing I'm sure he would think to.
Also, England was barely made for the attrition war that was engaged in 1420's and 1430's. While Charles VII was able to levy £ 800,000 in 1425 (550,000 from Langue d'Oil estates and 250,000 from the Langue d'Oc estates, numbers from Georges Minois' book), Duke of Bedford struggled to finance the occupation with in 1433 £ 80,700 spent for an income of only £ 64,800 (still numbers from Georges Minois' book). I imagine Henry V would have less difficulties to convince the Parliamant to raise the taxes he request, but that's still gives and idea of the difficulty.
Worse, even lands conquered in northern France were barely held, ripped by anarchy and banditry as with Normandy which was the place of important guerillas, or even Paris surroundings that were so much dangerous that it caused the decline of Paris. If the need is, you can still look at the coronation of Henry VI as king of France in 1431 to how much the situation was serious; barely crowned, he hastily rushed back to England, never to set a foot in France again.
Another advantage the Bourges kingdom had was technical and tactical advancement, especially in artillery, as with the Bureau brothers, while English army still stood by the same tactics from Crécy, Poitiers and Azincourt, too proud of its successes to mind changing until too late (IOTL, the consequence was the blitz reconquest of Normandy in 1449/1450).
