Henry V could very well have produced more sons too who also could have been more effective than older brother Henry was. However, the Dauphin Charles wouldn't have just passively allowed Henry V to reign uncontested, he would have tried to curry support for himself, the rightly born heir.
The most likely thing that happens is that Henry is able to raise his son partly into young adulthood, but a distant relationship, as Hal will be spending nearly the rest of his life in France fighting to keep his conquest, while Henry remains in England, surrounded only by his books, bibles, and prayers. However, Henry is able to be groomed correctly into a future king, a king who is more interested in peace and piety than war and chivalry. Whether he could still be a good king depends on who he surrounds himself with, starting with his marriage. More on that in a bit.
How does Hal do as a king with no war to fight? Even his early reign during a short peace was geared for war. Now he is a usurper, as far as most of his subjects are concerned. Now he has to consolidate his power and authority. It will be extremely difficult. We have no way to predict how good at this Hal can be. He will put down a ton of uprisings and revolts in a best case scenario. He would widely work to make alliances and play upon ever present French divisions. Can he reconcile two completely different nations together in a time when national identity was still taking it's first steps? I kind of have my doubts.
Charles VII needs allies fast, and if Hal is able to maintain his grip and see his heir grow safely into adulthood, how long are the other kings and princes of Europe going to stand by and let England, in effect, become OP? Let's see how good a diplomat and politician Charles can become in what is a much worse situation than OTL. He could see a fire sale on French land erupt before him.
What does Burgundy want to do here? They could perhaps finally see Burgundy break free of French vassalage and gain full independence. Or a more ambitious duke could decide to seize the French throne for himself somehow. They couldn't do either alone, however.
What kind of marriage options are there now for Henry? Depending on the advisors he ends up acquiring, or how close to his father's great project is his own goals are, Henry and his connections could strengthen alliances with Burgundy via marriage, could perhaps hope that a rich, landed heiress of somewhere like Brittany, Navarre, or further afield comes on the market, or they want to make a grand foreign alliance with the Habsburg-led Holy Roman Empire or with Castile or Aragon. Doesn't have to be Marguerite d'Anjou here, she might not even be in the running what with Henry's father likely negotiating the marriage instead.