That's not what happened. England was England and Normandy was Normandy. They never ceased to be separate entities and they still are today.

William was duke of Normandy, a region of France he held as the nominal vassal of the French king. In 1066 he conquered England, becoming both king of England and duke of Normandy. As king he had no overlord in England, but as duke he remained a french vassal. On his death he left Normandy to his eldest son Robert Curthose and England to his second son William Rufus. Robert went on the first Crusade, mortgaging Normandy to his brother William to pay for the venture. Then William died in a hunting accident and his younger brother Henry took the crown. When Robert returned from crusade, Henry fought him for Normandy, ultimately managing to capture Robert, who spent the rest of his days as as Henry's prisoner.

Henry arranged the marriage of his daughter Matilda to Geoffery of Anjou, another French noble who held the counties of Anjou, Maine, and Touraine, a large territory that bordered Normandy. By 1154, Matilda and Geoffrey's son Henry II was king of England, duke of Normandy, and count of the Angevin territories. He married Eleanor of Aquitaine, heir to a vast region of southwest France, making Henry the duke of Aquitaine. This is sometimes referred to as the "Angevin Empire" (for the house of Anjou) but it was not an empire in the sense of being one country with one government. Each region was separate with it's own laws customs and traditions. Each french territory had it's own arrangement of vassalage with the french king. Only in England was Henry II a king.

Henry's son John managed to lose Normandy and the Angevin territories to the ambitious French king Phillip II. The last bit of Aquitaine finally landed in French hands at the end of the Hundred Years War. During all this time, England never ceased to be England and Normandy never ceased to be Normandy.