Were Danes, who accompanied Rollie the Ganger in the ninth century when he carved off a bit of Gallia omnis, whose Latin was really going downhill anyway.
Like the Danes who occupied the English Danelaw, and gave us "drag" next to "dray", "draught", and "draw", "skipper" next to "shipper" and "ship", "clog" next to "cloy", and several other cognate pairs.
Ergo, no Frenchman ever ruled England, because the Conqueror and his seed weren't French, howbeit they may have worn the sprig of the broom and called it by a French name.
Well, now, I'd say that you are forgetting that it takes two to tango, or to make a child.
Tis true that the Norsemen landed in Armorica, attempted to take Paris and failed, settled in Armorica, and were granted a fief there by King Charles in 914 AD, swearing fealty to the King of France.
Tis also true that the Vikings did not have women on their longboats. They were like the Spanish, who sent soldiers into the Americas, not women. That there is a Spanish-speaking and cultured Latin America is because the Spanish men married with the Amerindian women, and the result is neither a Spaniard nor an Amerinidian, but a mestizo. Now cut off Spanish immigration and keep interbreeding over the generations, the Spanish element becomes a smaller remnant of the whole.
The Viking men settled Armorica and became vassals of the King of France in 914. They married French women. All of their children were half "French" (although there is not really such a thing as a French genetic race in the first place. "French" is the constellation of races and cultures that were under the King of France and were eventually united by a common culture and history into a people. The Kingdom was a very early and slower and more imperfect version of the American melting pot of cultures).
Christian religion was the common, uniting thread. The Vikings were not Christians, but their half-French offspring were, thanks to their French mothers.
Now reiterate that cycle for another 152 years, 4 or five generations, until 1066 and the Norman conquest of England.
And remember that new Vikings did not keep on piling into Normandy. What happened to the Vikings in France was the same thing that happened to the Hsiung-Nu and Mongols in China: the male warriors conquered, or took a piece of it, the Chinese or French females married them, and their offspring were of Chinese or French religion and Chinese or French language. Normans spoke French in 1066 and could not speak a lick of Old Norse.
If Viking males had been able to spontaneously reproduce over the intervening 152 years between their oath of fealty to the King of France and their great-great grandsons' conquest of England, had they brought vast boatloads of Scandinavian women, had they managed to preserve their religion, or culture, or even their longboats (the Normans did not invade England using Viking longboats), then you would have a point that Normans were Vikings and not French at all.
But reality is that, genetically, they were perhaps 15% of Viking stock (do the generational math), 85% French, 100% of French religion (and 0% worshippers of Wotan anymore), 100% French speaking (and 0% Norse speaking), their nobles were in the royal lines of France, and they considered France their kingdom, and vied for the crown along with the other French lords.
Certainly there was, and is, a distinctive Norman culture, just as there is a distinctive Breton culture, and Angevine culture, and Alsacienne, and Provencale, and Savoyarde. Indeed, there is no ONE French genetic race or ethnicity. To be French is not, and never was, the same thing as to be Swedish. Sweden is a land and a race and practically a family line. France is a Kingdom of many, many tribes and races that had a common religion, common language (over time), common law, and common King. Une foi, une loi, un Dieu, un Roi. Vikings were invaders from afar who were assimilated. Normans were as French as Parisians and Toulousains, and just as culturally distinctive as each of those three is from the other.