It only makes any kind of sense in the context of the times.
France in the '30s had been run by a left-wing coalition, the Popular Front (https://en.wikipedia.org/wiki/Popular_Front_(France)), which had put things like the rights of workers and a move away from laissez faire capitalism front and center. The head of that coalition was a Jewish socialist, Léon Blum (https://en.wikipedia.org/wiki/L%C3%A9on_Blum).
That in turn had led to a kind of mass freak-out among the French right, who were terrified that Blum and the Popular Front were the harbingers of a Russian-style Communist revolution. (They weren't, of course, but then as now the hard right can't hear a dog bark without thinking it's the first shot of a Communist revolution.) Even in 1936, when Blum came to power, there were people on the right saying things like "better Hitler than Léon Blum" (http://worldatwar.net/biography/b/blum/).
So when the Nazis blew the old government away, there were a lot of people on the French right who saw their country's defeat by right-wing foreigners as an opportunity to restore the old order -- things like favoring aristocracy over democracy, reserving lots of power for the Catholic church, driving Jews and immigrants out of society, and so forth. These people coalesced around Pétain, and their ideology became the ideology of Vichy's Révolution nationale (https://en.wikipedia.org/wiki/R%C3%A9volution_nationale). (One of the results of which was that Blum was hauled off to a German concentration camp.)