For France, it eventually comes to how and when Bourguignons and Valois/Armagnacs comes to terms. It was a consistent tendency, that Lancaster supremacy wouldn't really challenge (if something, giving Burgundy's ambitions, it may hasten it if Henry V stay in place).
Of course, Henry V's skills would make a reconquest harder, and while I don't see him managing to hold all of North-Western France (
1429 situation), I could see him maintaining his presence on Calaisis-Boulonnais, Aquitaine and Normandy (parts of it, or whole of it).
In another thread, I supposed a treaty similar to Brétigny or
Tours, meaning an official and plain control (without Valois suzerainty) of these holdings, at least before a second "Caroline phase", while I expect Henry V and immediate successors to deal better with it (namely, not letting it feeding factional infighting in England)
The key is how the english Parliament would react to 10 more years of Henry V that would be ITTL, King of France after the death of Charles VI.
French provinces would be supposed to bear the burden of the war, and while he benefited from better relations with the Parliament than his successors, he would have to face a similar reluctance : without clear gains for high nobility or parlementarian elites, he would have to live with limited French revenues (impoverished from war, as Normandy, or outright reluctant as Burgundy).
With his death, I suspect that the regency wouldn't be exerced by one man only, but more collegially with one Regent in title : Bedford, Salisbury, Gloucester,
Basically, as IOTL but more realistic with Henri VI being more in age to participe to politics. It would be interestingly similar to Charles VI of France's regency in this regard : tutelage of uncles with likely friction between them.
Would Henry VI tries to play Parliaments and favourites against them, or balance between factions is maybe a bit too far with the PoD, but open possibilities.
Personally, I would favour the first propositions, giving the OTL events.
Such a short regency would probably help to temporize in France : it's a thing to let things going loose for 15 years, but with a king being expected to takeover politically in 5 if not less years...nobody would want to take the responsability about loosing it all.
How does Henry's reign play out, and how does the short Regency of the 1430s work? Educate me!
Basically.
1) Late's reign is going to be a bit more hard than the part IOTL, but if Henry V tries to hold what he already have, the status quo could be maintained without Bourguignons shifting alliances. It means that the control on France would be limited however, and that he will still have to rely on Parliament for support, which is going to be harder giving the usual incomprehension ("Well, you have new lands now, so why don't you live with their revenues?")
2) The rengency, on this regard, would change little to Henry V policy, and while it may be a reasonable move for each regent's interests; it may be a bad move overall regarding Lancaster's interests. England managed to take the lead using civil war in France, and Henry IV having crushed opposition in England. Both weren't going to last, and Henry VI may face these problems on a not so good ground.