First, it's important to note that William wasn't simply invading England as a foreign conqueror, he had a strong, legitimate claim to the throne. Perhaps a slightly different example will clear things up: just imagine you are the son of a German Duke, you have gone off to earn a name for yourself and somewhere along the line you win a battle for the King of France and in gratitude he gives you a county as his vassal. Years later your father dies and you inherit his duchy. It wouldn't make any sense for the King of France to say that your inherited German duchy is now part of France, does it?

Also, these kind of 'feudal' relationships were much more fluid than people generally think of them.

William was King of England and therefore subject to no one in his English realm, but as the Duke of Normandy he was still a vassal of the King of France. There are numerous examples of this kind of complex vassalage - Duke A has a county in Duke B's duchy, Duke B has a county in Duke A's duchy so they are equal (as dukes) but are vassals of each other in their role as counts of those particular counties. So there isn't really a conflict that William (and his successors) were both Kings of England, beholden to no one, as well as Dukes of Normandy and vassals of the King of France.

It's also important to point out that the French king at this time was incredibly weak compared to his powerful nobles. Edward Peters lists the counts and dukes of Champagne, Blois, Chartres, Anjou, Maine, Normandy and Flanders as all being individually more powerful than the king. Even if the King of France wanted to make England part of his kingdom, there was no way he could force William (or his successors) to make that happen.