My understanding of it is that it's like any other invasion turned occupation turned integration. Some fast changes, some slow changes, lots of violence, lots of culture mixing. "Vikings" can mean a lot of different people, right?
In the sources, Vikings are sometimes called Northmen because they came from northern Europe. Northmen was then shortened over time to Normans. So sometimes you will see the word Norman used interchangeably with Viking even though those Normans have nothing to do with Normandy.
In 911, a group of Vikings led by Rollo negotiated from King Charles the Simple of West Frankia (France) the right to live on the southern coast of the English Channel. This area became known as Normandy - land of the Normans. In 1066, one of Rollo's descendants, Duke William of Normandy, invaded and conquerred England thus beginning the Norman period in English history.
William spoke a form of French, not a Germanic language. By invading England amphibiously William did demonstrate some capability with boats, but he and his army were nowhere near the sailors of his Viking ancestors. I do not consider William of Normandy to be a Viking although some of his culture was still Viking in origin. For instance, the Norman kings of England introduced jury trials into English law. Juries are Viking in origin.
Once they settled in Normandy, vowing loyalty to King Charles III they were no more Vikings, but they kept anyway the name that in the continent they gave them … “Normans” [and they gave the name to the region we call “Normandy”, for accuracy, not the other way round].
When the former Vikings expanded their influence to the isle of Great Britain they were “Normans”.
The Norse who settled in what would later be called Normandy were a minority that right from the start took Frankish wives or mistresses, including Rollo, who wed the daughter of a Frankish count. Because of that the Norse in Normandy very quickly went native.
By 1066, a century and a half after Rollo was named Duke of Normandy, the Normans had long since become culturally French.
If you're referring to the ethnic heritage of the Normans who crossed the Channel, it would have been a mixture of Scandinavian and French, much like William the Conqueror himself. Some of the "Normans" also weren't actually from Normandy. William's army included large contingents from Anjou, Brittany, Poitiers, and Flanders as well.
England was conquered by a French warlord leading an army that mostly French in composition.