I don't imagine they call him Prince William for nothing. I think we can all rest assured that Prince William is indeed a descendant of Duke William of Normandy. The Norman flag had an iconic cross that today shows prominently upon the Queen's diamond crown.
The Normans who invaded England in 1066 were of the same heritage as the Northmen (think Vikings). Norman derives from the word Northmen. Although the invasion was destructive, deadly to many English troops and King Harold, I've read that the Normans who invaded England in 1066 were mellower than the Vikings. History shows that the Northmen were violent invaders but settled down and adapted to the lifestyle of those they invaded. In the instance of Normandy, these Northmen had settled into the farming life of the area that is now Northern France and the men had taken French wives. It gets confusing if one desires to have clean-cut lines for culture and ethnicity but life isn't like that.
Suellen Ocean is the author of the historical novel The Celtic Prince and non-fiction Secret Genealogy II, Uncovering the Jewish Roots of Our Christian Ancestors, both available at Amazon, B&N and Ocean-Hose. http://www.pacificsites.com/~oceanhose/