Interesting discussion. First off, did England have any real support from the Nobles in France (besides Burgundy)? If so then they could pull off such a union. But if not then they'll be ruling on borrowed time. Second, what is the status of the French Nobility after the fall or Orleans? Are the opposition still organized or have they fallen into diss ray and only care about defending ther own lands? If its the first then the English will definitely have a problem, if not then they can take out each noble one at a time. Third, is Henry V alive in such a scenario or is Henry VI King? That makes a big difference. With Henry V there's a warrior King on hand to deal with problems and govern the Kingdoms. With Henry VI the Regency Council rules and that could be a problem.
A union born out of a military victory would no doubt be weaker then a union born out of a lucky marriage or being the closest heir (Anglo-Scottish Union). However, using examples in history from the Spanish Empire, its certainly possible. The Kingdom of Naples, for instance, was independent before being forced into Personal union with Aragon (later Spain). True, on the reverse end there's the eighty-years war that had the Netherlands broke away from Spain. SO IDK which way it would go. The King (Henry V or Henry VI) would have to rule from Paris, not London. France was the more populous, rich and really the more important of the two Kingdoms. Plus the King and generals would need to be on hand to deal with any possible revolts.England, on the other hand, was more centralized and the King seemed to be able to govern more effectively than in France. But of the two, I'd guess that it would be easier to put down a revolt in England than in France.