They would have to have had a great deal more success than OTL. It's possible the Free French wound up being led by someone less ... assertive than DeGaulle, which would have made them seem more like puppets of the UK and US (a charge that did get levelled a few times, IIRC) and the French Communists, after Barbarossa, started taking on the mantle of resistance to the Nazis. If the new governments were seen as less independent and less capable of standing up for French interests, a third force might have a chance.
This does raise the obvious question - if the Free French are beholden to the West, why should we overlook the French Communists being beholden to Moscow? The French Communists might try to claim they were independent and treat Moscow as an advisor, rather than a superior; how well this would go, in the post-WW2 world, is hard to say. It took a few years for the Cold War to get going and feelings about Moscow were quite mixed (still are). The French Communists might be quietly relieved there was a barrier between them and Moscow, in the form of a US/UK/USSR occupied Germany. However, they would be under immense pressure to deny transit rights and suchlike and there would be no way they could be relied upon if WW3 broke out.
Chris