If there was Joan of Arc and Henry didn't die in such an inoppertune manner, would the French actually accept the Treaty of Troyes and allow their throne to pass tot he King of England? Not asking about consequences; Just whether or not it would actually happen.
I'm assuming that you meant
no Joan of Arc. For starters I don't think she had that much influence on political events in France. As a symbol, yes she was very important, especially on the battlefield and perhaps to religious lay people who saw her as a reason for Charles VII's legitimacy. However, the noble supporters of Charles VII were actively looking for a reason to crown him, which they got after the Battle of Patay (1429), which Joan took no active part.
As to the second part of your question, I do think that the English cause would have been improved significantly if the English had gotten 10-15 more years out of Henry V
as well as the French getting at least another 3-5 years out of Charles VI. However , I also think that its important to remember that even though though the Dual monarchy was lead by a regency council, they were actually in a very good position in the early 1420's. Not only did the English control a but ton of France, they gained even more strength with the Treaty of Amiens in 1423 where Brittany and Burgundy recognized Henry VI as king of both realms. Also, in 1421 (I believe) a Paris court ruled that Charles VII had to vacate all of his titles.
What undermined the English position was the marriage of Charles VII to Marie d'Anjou (early 1420's), which gave him a strong power base and lots of supporters and the French victories in the Loire valley in 1429 which gave him the standing that he needed to really assert his kingship.
Long story short, with the stability and political unity on a continued reign of Henry V after 1422 would probably helped out a lot in the long run, making it plausible for a continuation of the Dual Monarchy, but Henry would still have to solve the war debt plaguing parliament in London as well as try to mitigate the aftermath of the Battle of Bauge in 1422 which decimated the English leadership in France right before his death.
Hope that helps.
