I think that when considerating Vichy state (called "état français" with no relationship with the previous republics) you should focus on how un occupied France the people were seeking for security (not considering the jewish point of view). There was a widely accepted idea of the Sword (standing for général De Gaulle and France Libre) and the Shield (with Pétain). In a lot of french families Pétain was a war hero that was trying to protect the population by collaborating with the nazis while it was helping France Libre. This idea was examined properly after 1970's Vichy France: Old Guard and New Order. 1940-1944 by Robert Paxton, which was a main historiographical revolution in contemporary french history. Hope this intervention will give you some answers as well as some tracks to find better answers