No, that is misleading. All of Europe (well, western Europe) had Celts in their lands at one time. But that is over 2000 years ago. The Normans are of Frankish-Norse ancestry. They were mostly 'Vikings' who'd been granted lands in Normandy by the French king, (land of the Northman) in return for keeping the entrance to France safe from other Danish and Norwegian plunderers. Rollo was the Viking who was given the land and he and his followers came en masse to Normandy to settle. They adopted French language and culture (especially the use of cavalry) but were mostly of Norse origins. When they came to England in 1066 AD under William, they were a mix of Norse and French genes...very little 'Celt' would have remained.
Check:
Vikings! "Fury fromm the North" (first 3 chapters)
http://members.aol.com/skyelander/menu15.html