Everything that I can find from googling indicates that William remained Duke of Normandy after becoming King of England. At this point in time, is Normandy still part of France, or was it considered part of English territory? Was the nation that it belonged to secondary to the lord that it belonged to? Was the King of England also a subject of the French crown during this period? Normandy is French territory today, but was that ever disputed by William's descendants? If so, how did the territory end up restored to French rule?
It was still part of France and the English king was in theory, the subject of the French crown as a result. If you look at what's anachronistically known as the Angevin Empire, you'll see that this was not the only territory held by the English Kings that was a fief of the French crown.
In terms of its reconquest by the French, this occurred from 1202-1204, where a French invasion successfully took possession of the land (as well as Maine and Anjou). The English would not recognise this officially until the Treaty of Paris (1259) so the question of the French holdings of the English Kings was definitely continuously brought up. Later on during the Hundred Years War, Normandy would be conquered during the Lancastrian period but would be lost soon after within three decades, and from there, it would stay French.