Socialism/Communism was a factor in pre-WWII France. The Germans had signed a non-aggression pact with the USSR and were, after all, Socialists, too. The French Left did not want to fight the Germans. And in May 1944 the future editor of the leftist newspaper Le Monde said that the Americans were the greatest danger to France, basically because they were not Socialists.
France was certainly a political quagmire for many decades in 20th century. The far left wanted socialism now, the far right was okay with anti-semitic views.
So how do you keep the country going when you have that kind of attitude among a significant number of the people? An evacuation to North Africa of some of the military forces would have been possible, but recall that the US had to fight those forces during Operation Torch. When the Vichy Air Force in North Africa was reequipped with P-40F's by the US, one pilot promptly flew his Warhawk to Occupied France
If France decided to fight on via evacuating to N.Africa, that means Vichy as we know does not come into existence.
US was not equipping Vichy Air Force.
My high school physics teacher was a USN aviator in WWII and was transferred to Pensacola. Getting his car to his new duty station was a problem and so the captain of a USN tanker headed that way offered to let the car be carried as deck cargo. The tanker was reassigned to Operation Torch and the French shot up his car; when he got it back, it was full of bullet holes and the top had been blown off.
In a shooting war, regardless how short it was, 'soft' vehicles have nasty habit to grow holes in bodywork.
As I see it, De Gaulle could have held Brittany and perhaps Darlan not Petain could have held what became Vichy. Darlan had the balls that Petain didn't. What are we going to equip their Free French Air Force with. So evacuation of factories around Bordeaux should be feasible. IIRC that Means D520. FF can still get Mohawk, Tomahawk, Maryland, Boston. Germans will still get all the way down to Biarritz eventually, although initially they stopped at Bordeaux.