There are some wrinkles to it all. What the Allies do in France can influence Axis decision making.
Some CW players do a bare minimum in France. They send Gort + 2 MOT to Calais, sit there and watch the Panzer parade to their south, never loan the French a single Pound, and then sail away again when the Germans have 2 hexes on Paris. All while building up the Royal Navy for the mid-game. And the French reward this by sending BPs to the UK when the Germans are adjacent to Paris.
Other CW players invest a fair bit more in France, and make sure the French have some ground units in production for the Fall of 1940, and have moved a couple factories to Bordeaux. A MTN unit and the 1940 French ART can make their mountain hex citadels pretty fearsome. Sure, they might end up as Vichy units. But they might not.
The question at hand is - are the Germans going to attack Spain? In the first situation, a weak France running low on units might be easy to conquer, without the US Entry penalty for collapsing Vichy. In the 2nd situation, the Axis calculus will be quite different.
Another possible Axis plan is to take Morocco. If that hasn’t been achieved when they have Paris, they may not wish to see Morocco become Vichy.
And another consideration is the utility of the French fleet. If the Axis can take Marseilles and Bordeaux from a lazy set of Allies, the French fleet will probably be out of supply and increasingly completely useless as it also couldn’t be re-organized (barring some heroic stand by UK infantry in Rouen, perhaps). In that type of situation, the French might choose to surrender France to pick a new Home Country - & thus a new Primary Supply Source. Though then a whole ‘nother turn would have to pass before the French ships could sail again, and their ships, wherever they might be, would have to trace a supply line to that new Home Country, wherever it might be.