Let's get this straight re: Henry V's death date. Henry died in 1422 after contracting dysentery IIRC from the squalor of the camps during the Siege of Meaux, a city in Ile de France. Henry V supported the Armagnacs as I recall, in agreement for full sovereignty of the English crown over Gascony, and totally against his father's will, since Henry IV was at the same time supporting the Burgundians. Indeed I'm pretty sure that at one point there were two English armies in France, both fighting for opposite sides. Henry V recanted his stance and rushed to his father's side to repent shortly before Henry IV's death but if his father doesn't look like dying then more such actions are likely to continue, with Henry pursuing his own policies against his father's will. I honestly don't believe that Henry V was a truly rebellious man who hated his father, rather a hot-headed man who seized opportunities and was too brash to back down at the first calling - so I doubt Henry V will spend all his father's life fighting for the Armagnacs but it changes the complexion of the war entirely. For a start, the claim to the French throne is likely to be butterflied entirely as it was entirely to do with how over-the-barrel Henry had the two French factions in 1414 and the Armagnacs had most to lose. In this scenario, we likely have the Armagnacs in a slightly stronger position thanks to Henry V's support for them on-off for a much longer position, and circumstances and the passage of time mean that the Armagnac-Burgundian dispute will likely peter out before Henry V ascends.
At any rate, the entire conflict has changed far too much for Henry V to be likely to catch dysentery again.
As per comments about rebellion brewing against Henry VI as a lame duck king...possibly, but bear in mind that in this TL, it's far more likely that Henry V has several sons, each of which will become a major supporter to Henry VI in the same way that the Dukes of Bedford, Gloucester and Clarence were Henry V's most trusted allies. Henry VI is not going to be an isolated figure dominated by his wife - in fact far more plausibly here his wife will be a supplicant woman from somewhere other than Provence - because his brothers will be the major part of his government and will be seen as a major column of support and a legitimising influence over Henry VI to any who thought of trying to have Henry VI deposed. Yes, it's possible that some of them will be...slow...like Henry VI himself, but genetics, history and chance suggests that Henry VI would have a couple of sound-of-mind brothers behind him.