Feudalism is indeed complicated, and a lot of what we imagine it was like is extremely wrong. The relationship between nobles didn't really have a strict hierarchy (count > duke > king > emperor) like we imagine, and there were situations where a king could technically be a vassal to a duke, or a king to a king.

In England, technically William remained a vassal to the King of France, Philip I, while using the title Duke of Normandy. This idea isn't really something we see often in modern media, that your fealty is based around a location, but indeed, William only really acted as a vassal while back home.

This doesn't mean he was loyal, as feudalism also didn't mean that the dukes respected their king or vice versa either. The Dukes of Normandy were always very independent, despite the French King's attempts to Frenchify them. At best, the Duke of Normandy remained an exceptionally and dangerously powerful vassal, at worst they were considered only nominally under the French King, if they were being generous.

This meant that even after conquering England, William came back to France and attempted to invade Brittany, and was effectively at war against his own king while still acting as a vassal through Normandy. The two made peace, and William and his children never formally reneged their position as vassals, though of course as time went on the two realms grew further and further apart. The only real nail in the coffin for England's link to the French feudal hierarchy was the Hundred Year War, 300 years after William's conquest, which ended with the English being driven from the country once and for all.

To sum it up: The Normans (and then English), before 1066 and up until the Hundred Year War were always nominally vassals to the King of France but in practice were almost always independent.