I think Rambo was being a bit harsh on the French and on America's military contibution in the war.
It is certainly true that many French collaborated with the Nazi's, and indeed some of the last units fighting in Berlin were French SS volunteers. Vichy itself was a national mistake of the largest order, and the actions of portions of the armed forces in fighting the Allies in Syria and North Africa now appears almost anal in its attempt to preserve 'French Pride'. However, the actions of the Vichy reigme has to be placed within the political and social context of French society within the 30's and the pre-occupation, shared with many in Western Europe, of Communism vs Facism. To many, better a Nazi than a live under Stalinist reigme.
More importantly it ignores the fact that the French resistance was the largest in Europe, and that along with the Poles, they formed the largest Free Armies serving in the Grand Alliance. Their sacrafice, when their own countries were occupied and being reduced to rubble, should not be forgotten.
It may sometimes seem that the USA is interpretated as buying victory with Economic power. This merely reflects the fact that the US under Roosevelt did become an economic superpower in WWII. Lendlease, supplies to Russia, the Liberty ships and even the post war Marshal Plan were all keystones to the Allied plan. However, it isn't meant to negate or ignore the bravery and sacrfice of American troops, who served as best as anyone in the Pacific campaigns, the D-Dya landings, the daylight bombing raids over Germany etc. The Bastards of Bastogne, the voluteers in the Flying Tigers, The Doolittle Bombers are all remebered for their bravery. It's just that from a strategic level, which is what the intial question was, the USA economic power was an undeniable factor. Anyway, people working 100 hour weeks in horrible dirty munition factories did their part just as anyway else did.