The Normans were ethnically a little of both, speaking French with a lot of loanwords. The same thing happened after the Conquest — they picked up and dropped off words from and into English, like ‘beef’ and ‘mutton’.
And SL, Britain is indeed one of the most invaded places on Earth, although there hasn’t been a successful one since the William and Mary’s “Glorious Revolution”. The old Celtic work “The Book of Invasions” more or less documents the pre-Roman invasions of the British Isles, and there’s a lot of time between the melting of the glaciers and the beginning of the surviving folk tradition for many others.
The Normans, their aristocracy anyway, were largely Norse in ancestry, though probably mostly on the paternal side. Probably acquired wives locally, for the most part.
By 1066 they’d become more or less indistinguishable from the native French around them culturally and linguistically over the 150 years since they settled in Normandy.
But given their multiple conquests from Ireland to England to Italy to Palestine, it’s pretty clear that the Normans had a “fire in the belly” unmatched by any other region of France. It’s difficult to not assign some sort of ethnic component to it.