I voted that France could have been persuaded to join the Axis, and that this could have affected the outcome of WWII.
The key psychological moment was when Britain attacked the French fleet. Imagine this scenario: a day or two after that attack, Hitler approaches Petain with a proposal. France becomes a full member of the Axis, and declares war on Britain. In exchange, Hitler returns Paris to French control. (While maintaining German occupation over most of the rest of northern France.)
The second step in getting France to fight for the Axis would consist of returning the rest of northern France to French control in exchange for a French declaration of war against the Soviet Union. Plus a major troop commitment to that front, to prevent the declaration of war from being a mere formality.
I’m less than 100% certain that the French would have accepted the above-described offers. But I feel those proposals would have represented Germany’s best chance for getting France to fight for the Axis. (Especially if they were coupled with promises of French acquisition of British colonial territory in Africa.)
As for the idea that France would never fight against the Western democracies or in favor of the Axis: it did both those things in the early stages of Operation Torch. The United States lost about 500 soldiers fighting against France; and France lost over 1300 soldiers fighting against the Americans. On the surface, those numbers imply that American soldiers were about 2.5x more combat-effective than the French. However, other factors may have contributed to that seemingly one-sided exchange ratio, such as Allied air attacks against French soldiers. But even if that 2.5x ratio is an accurate assessment of the relative combat effectiveness of French and American soldiers, it still would have meant that French soldiers would have been about as combat-effective as their would-be Soviet opponents.
France deployed 144 divisions in the Battle of France. It experienced 360,000 dead or wounded, and 1.9 million captured. In other words: the vast bulk of French soldiers had not been killed or injured, but rather were in German custody, or else had escaped either fate and were physically located in Vichy France. Given those data, Vichy France could have assembled about 100 divisions for use against the Soviet Union. Also, French artillery was very good. French tanks were not particularly mobile, but were heavily armored; and would have been useful in the “heavy tank” role in major battles.
By the late fall of '41 the Red Army consisted of 600 divisions, about 400 of which were deployed on its western front against Germany. (The others were either on its eastern front to guard against Japanese invasion, or were in training/reserve.) Due to steady losses, its usual size would be 450 divisions–with 500,000 men added each month to replace losses. In the summer of '41, the German Army consisted of 150 divisions–100 of which had been sent east to fight the Soviet Union.
German soldiers were even more combat-effective than American soldiers. To the extent that Operation Torch was an accurate reflection of French soldiers’ combat-effectiveness, those 100 German divisions on the eastern front would have been much more valuable than 100 French divisions. However, Germany came very close to taking Leningrad in '41, and came close to taking Moscow later in ‘41. Perhaps 100 extra French divisions would have made the difference between failure and success. The fall of those two cities would have weakened Soviets’ ability to resist the Axis in ‘42. That–plus the benefit of French support–could have paved the way for a successful Axis invasion of the Caucasus and its oilfields. With Leningrad, Moscow, and the Caucasus in German hands, Hitler would have been in position to negotiate peace terms with Stalin. Stalin might well have agreed to peace, on the theory that 1.5 years of war would have brought him nothing but losses, and on the theory that the loss of Moscow’s industrial capacity and the Caucasus’ oil would have rendered future victories far less likely.
The French naval presence could also have had an impact on that eastern front. One of Germany’s biggest problems was the British food blockade. The French navy could have helped it break that blockade–at least in the Mediterranean. While the breaking of the blockade in the Mediterranean alone would not have solved Germany’s food problems, it would have made the food situation somewhat less dire. In the actual war, the dire food situation in German-occupied Soviet territory seemed to reinforce Soviet claims that the Germans had launched a war of racial extermination. If the food situation in those territories could have been improved upon, the German invasion might have seemed like a liberation from the brutality and terror of Stalin’s evil regime. Even with the food situation as bad as it was, 1 million Soviet citizens served in units directly or indirectly controlled by the German Army. Boosting that number to 2 - 4 million could have significantly altered the situation on Germany’s eastern front.
