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 an 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).
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?")