^^
When someone is really mixed it can indeed be difficult for these companies to get it right. It winds up that only people with all four grandparents from one place are correctly labeled, and they usually don't need a test to tell them their ancestry.
That said, companies should do a better job on people who have 50% ancestry from one place. That's one of the reasons I'm not fond of ancestry.com. It doesn't have a history of doing a good job for those people, in my experience. Have you done 23andme? The people I know who are half Italian, or at least half southern Italian, usually get decent results.
I think ancestry does a really bad job with Northern Italians/Tuscans in general. In my prior version they had me as 45% French and 55% Italian. That's obviously silly, since I know my ancestors have been in certain specific areas of Italy for at least 900-1000 years, and probably much longer than that. If I were adopted and didn't know my genealogy I could be thinking one of my parents was "actually" French.
Now it has changed. The French has gone down a bit and I gained maybe 5% Greece and Balkans. Still wrong, but whatever...
As you can see, this leaves far Northern Italy and Provence sort of in limbo, like, I might add, Normandy and Brittany and Picardy and Alsace in France as well.
When I look for more detail on my supposed "French" ancestry, this is what I see:
This time the quasi French ancestry takes in a piece of Switzerland, which makes sense, all of Northern Tuscany, and Catalonia as well.
Fwiw, I've been saying for years that I thought that there was a genetic link between Liguria (and northern coastal Toscana), the French Mediterranean Coast, and Catalonia. I've traveled that coast innumerable times, lived for a while in Barcelona, go to Provence every year, and see it in the food, the similarities when people speak in dialect, even in the "look" of the people. Now genetics seems to support that.
Perhaps it goes all the way back to Cardial, then to the Ligures, then the Romans/Greeks. I don't know, but it's there; slightly different proportions, but still there.
To call it "French" is a little much, though.
Interestingly, although ancestry sees me as part French, all my ged match calculator results see my closest populations after Northern Italy and Tuscany either as northern Balkans like the Bulgarians, or Spanish.