[Atlantic Friend]

"The Normans are the descendants of Vikings, they may have spoke French, but they are not French."

Well, as you probbaly know, there is no such thing as an ethnic French, as in our veins runs the blood of Celts, Wisigoths, Normans, Romans, and various Germanic tribes. Ethnic purity is usually seen on insular populations (and wannabe Nazi regimes of course)

[Vicomte13]

"The Normans are the descendants of Vikings".

They are the descendants of Viking men and Gallo-Roman and Frankish women. Since no new Vikings came after settlement, the Viking element was much attenuated several generations later at the Norman conquest.

Vikings did not bring shipfuls of women on their wars.
The first generation were mostly 50% French, 50% Viking, with the Viking element diminishing rapidly. The Normans were French like the Manchus are Chinese.