That's nice but let's begin by noting that Dukes are not Kings. As you correctly note note King Henry II married Eleanor of Aquitaine; upon doing so her name and title did not become Eleanor of Normandy, nor did Aquitaine thereafter become a part of Normandy. Aquitaine is Frankish (from which the term "French" is derived) and Basque if anything. Not Norman. Not Scandinavian.
The original poster wrote: "Recall that the Normans from french Normandy invaded England and defeated the Anglo saxons.
I think we can agree that there was no such thing as a "french Normandy" at the time of William the Conqueror and that Henry II did not show up as a regent of the Normandy region until over 50 years after William the Conqueror's death. While Anglo-Norman regency rivalries certainly transpired during that time between the death of William I and ascendancy of Henry II, Aquitaine never became a part of Normandy, particularly where being "french" has anything to do with it.
FReegards!
Julius Caesar's Commentaries on the Gallic War starts out:
Gallia est omnis divisa in partes tres, quarum unam incolant Belgae, aliam Aquitani, tertiam qui ipsorum lingua Celtae, nostra Galli appellantur.