Well, that's not true. The original inhabitants were what we'd call French. The "North men" that gave their name to the duchy were Vikings who first appeared up the Seine in 820. Over the next century there were several raids and a growing presence of "Norse men" settlements. Charles the Fat, great-grandson of Charlemagne, paid off the vikings as a way to deal with the raids. He was deposed, and the throne (eventually: Ode of Paris got it for a few years) went to his cousin Charles the Simple, who made a more permanent solution.
Charles negotiated peace in exchange for lands, and offered his daughter Gisela to the viking leader Rollo, who would be named a duke and swear fealty to King Charles. Rollo's children would be the ruling dynasty in the new duchy named Normandy. (The illustration is a late 19th-century idea of what Normans looked like.) An 11th century Benedictine monk, Goffredo Malaterra, writing about the Normans inroads into Italy and Sicily, described them:
Specially marked by cunning, despising their own inheritance in the hope of winning a greater, eager after both gain and dominion, given to imitation of all kinds, holding a certain mean between lavishness and greediness, that is, perhaps uniting, as they certainly did, these two seemingly opposite qualities. Their chief men were specially lavish through their desire of good report. They were, moreover, a race skillful in flattery, given to the study of eloquence, so that the very boys were orators, a race altogether unbridled unless held firmly down by the yoke of justice. They were enduring of toil, hunger, and cold whenever fortune laid it on them, given to hunting and hawking, delighting in the pleasure of horses, and of all the weapons and garb of war.
The first sentence suggests a culture that would fight internally for a better position, which supports William of Poitiers's comments about rebellions in Normandy. Of course, in the 1060s, a Duke of Normandy would decide that England owed him their crown, but that's another story.
Sticking with the beginning of Normandy, we should look at Rollo and Gisela and their children; except that they had no children. The reason why they had no children is likely because Charles' daughter Gisela did not exist. I'll explain tomorrow.