Ok, I dunno... But in the timeline Hitler and the nazies are dead, so no aggressive xenophobism, only "regular" xenophobism. And Mussolini failed his fast and easy coup, we could guess that his group scattered throught Italy and fled to neighbouring countries including France, spreading the Roman Fascism ideals strenghening the Republican ideas of the Croix de Feu and giving integralism, the social fascism mix, a real ideologic base.I said the Republic rather than republics in general; I'm agreeing with you My concern is over the points of policy that he would support, as in my understanding he was very prepared to work with various xenophobic groups and supporters until his alignment behind the Republic.
If La Roche gets to power with the integralist or not, he wont have this kind of problem as he was a fervent catholic. IRL he founded a new social christian conservatist party in 1940. And well the pope has bigger fishes to fry ie the italian civil war with leftists in both camp + world anarcho socialist rebellion...I don't think "integralism" would be involved in that scenario, though, seeing as French integralists would still be facing the problem of the Papal interdict.