France surrendered to the Nazis in 1940 for complex reasons. The proximate cause, of course, was the success of the German invasion, which left metropolitan France at the mercy of Nazi armies. But the German victory opened profound rifts in French society. Instead of fleeing the country and keeping up the fight, as the Dutch government and a residue of the French military did, the bulk of the French government and military hierarchy made peace with the Germans.
But what if key figures (such as Marshal Philippe Petain) had viewed the situation differently? If the French government had decided to go into exile in the Empire, rather than re-establish itself in the German protectorate at Vichy, then the rest of World War II might have gone very differently.
France had extensive assets available to continue its resistance against the Axis powers. The French Fleet was the most notable of these; France possessed two of the world’s most modern fast battleships, numerous powerful cruisers and destroyers, and a host of support vessels. Had the French acted with any speed to the success of the German Ardennes offensive, this fleet could have evacuated a substantial portion of the French Army to Britain and to North Africa, possibly with much of its equipment intact.
In Allied service, these ships could have helped hem in the Italian Navy, and cut Axis supply lines to Africa. Against Germany, French squadrons could have hunted raiders, driving the Germans to the Arctic even before the entry of the United States. And when war came to the Pacific, the Fleet could have deployed in defense of French Indochina and other French possessions, as well as giving critical support to the Royal Navy. For their part, the Army and Air Force could have contributed to the war in the Mediterranean, the defense of Greece, and to resistance against Japanese encroachment in French Indochina.
In Africa, while we can assume that the problems that bedeviled French-British operations in France would have persisted, the continued resistance of the Empire would have put Italy in an untenable position. Italy struggled to supply Libya when faced with just the British; the presence of the French fleet, as well as an active military threat in Tunisia, would have made it very difficult for the Axis to sustain operations in Africa.
Given the lukewarm Italian enthusiasm for the war in the first place, a concerted Franco-British offensive in the Mediterranean might have pushed Italy out of the conflict early, or at least curtailed Rome’s contribution to the Eastern Front. If Mussolini persisted in foolishly declaring war on Greece (as might have happened in case of the loss of Libya) French and British forces together could have sustained a serious Greek war effort, although probably not enough to hold off the Germans.
In the Pacific, Japan occupied French Indochina (first in part, and then wholly) because of the collaboration of the Vichy regime. Had the French government remained at war with Germany, authorities in Indochina would have had both the means and the motivation to resist Japanese advances. Unless Tokyo was willing to risk an early war with the British (and possibly the Americans), it would have needed to seize French Indochina in the first days of its December 1941 offensive, which would have significantly delayed Japan’s larger offensive into Southeast Asia.
On the Other Hand…
The biggest reason that many French decided to collaborate with the Nazis was fear of what Germany would otherwise do to occupied France. To be sure, the Germans took great care in 1940 and 1941 to assure the French of their (relatively) benign intentions. At the same time, the Germans looted what was left of the French military and the French treasury, funding the Nazi war machine as it undertook campaigns against Britain and the USSR. Still, France mostly avoided “Polanisation,” the complete destruction of the national unit that the Germans carried out in the East.
Without a Vichy, the situation might have gone much worse for France, especially if the military continued an effective resistance from the Empire. The Germans always found some collaborators, and whether or not the French government continued to resist, some local authorities would have cooperated with the Nazis. But conditions in the occupied portions of France were worse than in Vichy, especially for those (Jews and political opponents) specifically targeted by the Nazi regime. In the south, Mussolini’s Italy might have been able to carve away a bigger chunk of France that it eventually took control of.
The availability of French territory in Africa might have made both Franco and Hitler more amenable to each others’ entreaties, although much would depend on how effectively the French and the British fought Italy. At the extreme, persistence of French resistance in Africa might have forced Hitler to delay his invasion of the Soviet Union, although even in this case Germany lacked much in the way of means to bring the British and French to heel.