I played a game as the Allies against the Hard AI with out of box rules and removed everything from France before the first turn, including all facilities in their territories (losing the facilities probably hurt the Axis more than the Allies). The British troops in Paris stayed, however.
I won as the Allies.
Granted, the AI’s play as Japan was a disaster (it’s generally a tough country to play and other AIs have performed even worse), but I made my fair share of mistakes out of carelessness and rushing, and their play as Germany and Italy was mostly solid.
The lack of French troops allowed Germany to declare war on the Soviets G1 and advance quite quickly. The Soviets were definitely in danger of collapsing the first 10 turns were it not for massive amounts of support from the British. Still, the Allies barely weathered the storm and were able to slowly push the European Axis back, with the US making frequent-large scale landings on the Western Front, eventually capturing Rome (the Axis navies and air forces in Europe were negligible). The UK did not participate in many landings, focusing their efforts on a successful strategic bombing campaign and continuing to funnel troops onto the Eastern Front from industrial complexes in Egypt and the Union of South Africa, where they ended up doing 30-40% of the fighting there.
Thanks to the aforementioned poor Japanese play, UK Pacific and China steadily dismantled the Japanese presence in Asia, while the Allies achieved dominance in the Pacific within the first 10 turns.
Overall, while the Allies were able to win without France, the loss of all those units hurt the Allies more than expected. In a competent player’s hands I think the Germans had a better than even shot of capturing Moscow early on.
Full game: