Ah, right you are. Though in fairness the priests in France would be intrinsic to any client theocracy. Though they’d likely arrest dissenters claiming they were heretics.Will look what Hitler did with Poland. The regime he put in there claimed to be democratic, and yet still arrested many priests pretending they were “Socialists”. That’s the main reason the regime would eventually dissolve
Honestly the biggest question would be how long it would last against a revitalised Britain and a post depression USA. FDR has been called a Ceasar, but Augustus fits better. He led the nation with a firm hand of steel, but cooperated with the constitution and proved a marvellous commander in chief when Japan attacked Pearl Harbor. I don’t doubt militarily Crusader France could hold off one or the other, but in the 30s and 40s, War with Britain was war with America and vice versa.