Actually, beignets exist in the same doughnut form in France, I read briefly on that, they are believed to be originated in Ancient Rome (some talked about Spain, and even Middle Eastern origin). I know that there a few regional variations here in France.
One variation is called beignets de carnaval or nun’s puff or better, nun’s fart (pets-de-nonne), they are largely consumed in Mardi Gras during Epiphany.
I have never thought of making them as they are available in many bakeries here.