Suppose Henry V lives another 25 years?
Suppose Henry VI is physically and mentally healthy?
Suppose Henry VI is physically and mentally healthy?
For one thing, no Tudors (or rather none in OTL form, so Maggie B. will have to be married off elsewhere). For another, it's unlikely that Henry VI will be his father's only son, or if he is, hardly his only child. So I agree, (very unlikely) the War of the Roses are gonna happen when and where they did.
Also, IDK what Henry V's stance on the Beauforts was, but they might not be brought into the line of succession if Catherine has more children (particularly boys) by Hal.
I think the idea that the French will get pissed off with foreign domination and will successfully revolt is unsupportable, did the Anglo-Saxons kick out the Normans in the aftermath of Hastings? Did the Occitans kick out the Northern French in the aftermath of the Albigensian Crusade? Did the Rhomanoi kick out the Turks in the aftermath of Manzikert?
If Henry V is alive and healthy when Charles VI dies then he will succeed easily as King of northern and western France, he's been acting as King for 5 years now and while he still hasn't completely secured the area he's solidifying his position. Southern France meanwhile is effectively a separate realm and under the control of the Dauphin/Charles VII who will as in OTL refuse to accept his disinheritance and will revolt. As to how the resulting war will go I'm not sure, in all certainty Henry V's control of northern France and England, his alliance with Burgundy and his greater military experience should see him win. However Charles VII was an extremely canny King if not a great General like Henry V and Charles has firmer control of his realm than Henry does of his.
Still lets say after another decade Charles VII is dead or exile and Henry V is ruling from Paris, France is under the control of either French nobles who have accepted Henry's rule and fought alongside him for over a decade or Englishmen who have been granted French holdings. Now the different nature of French feudalism means Henry is weaker and less absolute as King of France than as King of England and the nobility more powerful. So he, Queen Catherine and their children will spend the vast majority of their time in France even after the Dauphin has been defeated. Now when Henry V dies leaving an adult heir born and raised France who the key France based nobles will have known for years he will be easily acknowledged and recognised. Especially if Henry V has resurrected the old French practise of having his heir crowned during his lifetime.
However ruling such a massive Empire stretching from Marseilles to Carlisle is going to be a nightmare, the distances are vast and the communications technology dreadful so Henry VI is going to face internal problems, problems exacerbated by Spain and the HRE who will be worried about having such a colossal Empire on their borders.
Add to that Henry VI is going to be a French King, he will have been born and raised their, his family originates in Anjou and the fact that France is bigger, richer and more populous means he will spend the vast majority of his reign in France and will only rarely cross the Channel. Its not difficult to imagine that after a generation or two you might have a Plantagenet King who doesn't speak English, couple that with the possibility of the Renaissance boosting nationalism and the Reformation giving an excuse some future Duke of York or Earl of Warwick may well lead an English revolt to re-establish an independent Kingdom of England from French dominion.
Much like the Spanish Netherlands which went from being Emperor Charles V's homebase to in nationalist revolt against his son.
If Henry V lives longer he will have more than just northern France to pass on. From the Treaty of Troyes in 1420 to his death two years later he was constantly fighting against the supporters of the Dauphin to cement his claim to the Throne of France and he was doing well. While of course the Dauphin/Charles VII could stage a comeback like in OTL I think it's doubtful that as Henry V wouldn't have the same problems that Henry VI's Regents did. Anyway even if there is a division between northern and southern France northern France will keep the name France while southern France will become Aquitaine or Occitania.
Ok so we'd have Henry VI in France, Charles VII in 'South France' (eventually the Kingdom of Aquitaine and Charles as Charles I of Aquitaine) and John II of England (Henry V's second son, named for John of Gaunt).
Sound good?
Say hypothetically Henry V lives another 20 years and has more children with Catherine of Valois. Even if OTL Henry VI lives, would the possibility of him taking vows as a priest be off the table? Say he and his family realize that he didn't have the makings of a semi-competent king? OTL Henry VI was often described as being more suited to be a priest than a King, so I wouldn't be surprised if he went along with the plan. Also I think he continued to fight for the throne during the WoftR for his son's sake not his own.