Yes, and that was in fact the plan.
The Battle of France was lost due to an improbable amount of disastrous coincidences, from multiple poor political decisions by many Allies to German battle plans falling into Belgian hands driving them to do something very stupid (the Ardennes gambit) to very bad (and in one case, probably treasonous) decisions by some French generals to the British general ordering the BEF to run like panicked chicken towards Dunkerque right when the French counterattack would have crushed the overextended German forces...
But even after all that, France still had plans to continue fighting. The idea was, give up metropolitan France - apart from maybe the Alpes, it could simply not be defended with what little forces were left - and keep fighting with the resources of the Overseas Empire, especially North Africa.
Already in WWI, France had largely drawn from its colonial empire for soldiers to send to the meat-grinder of the Western Front as soon as it became apparent that they needed more men. Unlike British or American forces, the comparatively lower racism level allowed Home and Colonial troops to fight alongside well, and war propaganda even helped build the image of the vaillant colonial forces. To the point that to this day, the Tirailleurs Sénégalais are still remembered in France. This time, given how fast the disaster unfolded, there was basically no time to send colonial forces back, however, but the colonies were already on war footing, and ready to defend themselves - which they later did with success, in fact, though against the British (before switching sides to Free France - yeah, the whole thing was kind of a mess).
150K French soldiers had been evacuated from Dunkerque, and those would have been sent to Algiers to be reorganized and rearmed. Parts of the French Navy were already in North Africa, the remainder could complement them, go to British ports or even be sent to Indochina. There were already colonial troops mobilized, and looking at WWI, many more could be raised as needed - and that's without talking about the volunteers that would have left France for French North Africa and take up arms under a legitimate fighting government.
While industry would have been a problem, reserves would have been enough to go by until US imports started to make the difference, as well as building new factories there to an extent.
The French Navy would have probably been enough to shut down the Axis in the Mediterranean, possibly with ships to spare. This would have freed the British up for the Atlantic, and considerably accelerated the fall of Italy - though a naval landing would still have taken years of preparations. (Historically, most was either stuck in France and later scuttled by its sailors instead of letting it fall in the hands of the Nazis, or murdered by an early British sneak attack while the sailors were, in fact, in the middle of scuttling it themselves, so it was not much of a factor on either side later.)
France had possibly the best mountain troops of the entire war, some very well trained pilots and one of the greatest (and the most underrated) general of both world wars at the new head of the military, once they had, like in early WWI, fired the incompetent generals they had let taking things over because of politics.
At this point, they decided that they needed to give someone emergency dictatorial powers to see the crisis off without being bogged down to politics. After all, if it worked for the Romans, it should work for them. So they picked the Lion of Verdun, a legendary general of the previous war and respected by friends and foes alike. What could go wrong, right?
Well, it didn't always work for the Romans, and the guy they chose was very old, loathed politicians in general, was and too easily influenced by the local fascist strain. Which is why this plan spectacularly backfired, with the new government saying fuck you to the British, let it burn to democracy and more or less switch sides to the Axis and make a mess of things like you would expect from Mussolini copycats.
So yeah, totally believable, except a believable scenario would never have gotten far enough for the Allies to actually loose the Battle of France.
But you know how it is, the studio had said that the bad guys should win, and they were writing by committee against a deadline, and we all know how those scenarios turn out.