No, England has never been part of France. William was Duke of Normandy. The Normans were not French, they were Norman. At that time the Kingdom of France did not include Normandy.
William did seek to eradicate traditional Anglo-Saxon culture after the invasion, it was at the expense of Norman culture (eg, he installed several Norman Earls and Barons as landowners in England) rather than French culture. England was still England; it was never subsumed into Normandy or France, but had a Norman king. He ruled as King of England, and was also still Duke of Normandy; he kept the administration of his 2 territories separate, so William never even made England part of Normandy let alone it being part of France.