By this logic Sicily should be ethnically Normand, but obviously it's not, they are still each pretty much at the opposite end of Europe's genetic. Yet they ruled it for more than a century. No more than Corsicans since 1786 magically morphed into another ethnicity when the island became French.
However we know Nice and a tiny area around is ethnically Italian, since... it has been through most of its history an Italian city next to the border called Nissa, that's even where the so called Provencal sample was taken from but it's clearly Italian as expected, more so than even people from Aoste despite them living in Italy (they are part French at the very least). There has been so many Kingdoms and change of rules in Europe, for the most part they are ethnically irrelevant as they were just rules and papers, not population movements.
France continuum is more a West/East than North/South divide with a few exceptions, genetics clearly showed that in many studies.
My own results from the southeast, mostly Isere (1/2), with Provence and some minor Burgundy for the other half. Ironically the Provence side is the most northern plotting of them all, and extremly far from the "Provence" sample of Nice.
https://i.postimg.cc/BJYXZmLC/bAM158H.png
Very Sardinian indeed. At this very zoomed scale, Sardinia would be in another room outside of your computer screen.