And there was the Auld Alliance which could have made things worse.
Not necessarily.
A dynastic union isn't impossible per-se, and you could have some interesting PoDs.
I don't think HYW would be one of them, honestly.
Even if Valois dies out, or are unable to hold a claim ITTL, Joan of Navarre would be favoured rather than Plantagenets, for diverse reasons (the lesser not being she had superior rights).
Lancaster takeover seems really unlikely depsite their victories. Still, with a really really big lucky rap, they may hold it.
Another possible PoD be Louis VII of France being crowned as king of England. He came really close of that
IOTL after all.
I'm not sure Capetians could hold it definitively, though, as the english nobility rebelled more against John than in favour of Louis.
He may as well be an Henri V equivalent, while I think he had more chances.
(Auld Alliance wouldn't play, for the simple reason it didn't existed yet).
Scottish interference, one way or another, would be quite limited anyway.