I didn't read the paper yet so maybe there's an explanation, but the findings for places like Argentina seem completely off. The impact of Italian migration there is much bigger than that.

The figures for the U.S. are also absurd. There is nowhere near as much French ancestry as that in the U.S. It's mainly some French Canadians in the Northeast and upper Midwest, and the Cajuns.

I don't know these authors, but something is really wrong with their analysis. No one should take these results seriously.