You'd probably end with a more important repression of Hotspur's rebellion, but overall little to no changes on the court. I won't see Thomas having a much different policy than his father.
The possibilities of a revolt of his other brothers isn't to be ruled out, but I'm not sure they would have nearly enough support to be more than a nuisance.
Regarding France :
It's probable that Thomas would still try for campaign there as he did IOTL. Probably in the same mood than Henry : not trying to claim the crown, but raiding the hell out of the coast and make a safe loot.
It may be located more on the general Atlantic coast than focusing on Normandy, however. Thomas seems to have focused on the old duchy IOTL, and would try to grab it with supporting either Bourguignons or Armagnacs in the ongoing civil war.
It's probable that he could take Aquitaine (Such conquest would proove easier to be kept than Normandy, as you had local support there up to the very end IOTL) as he wanted, but probably more by diplomacy than battle, he doesn't seems to have been that bright as a commander (even if his death at Baugé overshadow it).
He seems to have been more conservative than his brother on some features, so I'd see a maintain of old practices : ransoming prisoner instead of killing them, namely.
Would England be able to hold Aquitaine? I don't think it would be possible on the long run : each time the kingdom of France managed to get its shit together during HYW, it managed to win what was basically a war of attrition. But it could hold at least long enough to crave some sort of equivalent to Pale of Calais that could be maintained longer than Aquitaine per se.
There's also the possibility of an english defeat in a campaign. That's gonna be a huge boost for whoever have the lead on the royal french court (probably Armagnacs). I won't see a campaign against England lands in France, not immediatly at least :
France itself is gonna be troubled more by the civil war, maybe longer than IOTL. English advance prooved a really good basis for reconciliation.
Cabochiens revolt wouldn't be butterflied, meaning Armagnacs would be controlling Paris at this point.
It mean that
Louis de Guyenne may survive and inherit. It seemed experienced enough, but without a great hold on events : that said, so was his younger brother and he was clearly less experienced.
Psychologically, he looked a lot like his grandfather, Charles V. It may be of good omen, or not.
He,basing myself on his behavior, may have tried to play each faction against the other, beneficing to have Burgundy as his father-in-law, and impose the royal peace. It's not going to be really easy, and I'd see him pulling a Charles V : buying peace with England at the cost of Aquitaine, beating the crap out of feudal factions, acting against England.
It would also wipe out the Tudor Dynasty.
Fair point : Tudur dynasty would be barely remembered as taking its part into the Welsh rebellion.
Catherine could still be married to Thomas I in this case. But instead of a Treaty of Troyes, it would be just a typical dynastic marriage, like Edward II and Isabella of France.
I don't think so : Isabelle de Valois was indeed married with Richard II, but in a context where peace seemed to be installed in France between them. Neither Henri IV or Thomas proven to have that in mind, at the contrary.