As always in this sort of thing, a lot depends on how loose your tolerance for anachronisms and other small inaccuracies is,but to my eye, it's probably close enough to pass. For my part, at this scale, I think the helmets, any distinctive weapons, and uniform colours go a long, long way toward "selling" the illusion as long as the general outline of the uniform isn't too far off.
In this case, I think the puttees, loose trousers, short jacket,and webbing for both the WA WWII Italians, and the French army in 1941, look pretty similar to each other - those Italian uniforms look pretty generic, really, and I think they could probably be used for a variety of different European armies in WWI-WWII.
It's really a "Your Mileage May Vary" situation, though, beyond a certain point!
I'm no expert or historian, so take the following with a grain of salt:
Apparently the French had trouble producing their own cloth for uniforms through the war, and early on imported cloth from Britain, in a khakhi/"mustard" colour; it seems the distinctive blue colour they used in WWI wasn't very practical for actual battlefield use, and went the way of the British "red-coats" sometime in the '30s. It looks like the WWI French helmets carried over at least into the early '40s (and these helmets were apparently pretty popular with a variety of European armies!)
With that in mind, I think you might also be able to get away with using WA's upcoming WWI British kit as a base for your WWII French, instead of the Italians: not sure whether it was just the cloth supplied by the British to the French, or if the British actually made the uniforms, but to my eye, the British uniforms look very similar to both the French and Italians, and the British uniforms might even be more correct for the French (though to be honest, I think either would work just as well at this scale.)
At some point, in the late war in retaking France I think, the French apparently imported American uniforms, helmets, and equipment, and it's possible that you could get away with using some WWII Americans as the base for your project, depending on when your WWII French army is active.
The French Resistance kit might help provide some of your weaponry - most of the guns from your WWI French ought to be correct, and, from the Resistance kit, it seems the French in WWII would have also used British SMLEs and Stens, FM-24/29s machine guns, Berthier rifles, the revolvers and semiauto handguns, and the spherical F1 grenades. The French also used captured German and Italian weapons.
The soft garrison/overseas/side-caps in the French Resistance kit were apparently also correct for military uniforms, and I kind of get the impression that some of the French Resistance outfits are actually designed to be French military uniforms given a bit of a civilian make-over when French military surrendered - these might come in useful, depending on your army's story and what point in the war they are meant to be fighting. (The berets in this kit are cool, and might also come in handy: it was apparently part of French military uniforms since the late 1800s such as the Elite Mountain Infantry, and was also symbolic of the French Resistance through WWII, so I expect a beret or two wouldn't be out of place on French soldiers rejoining the army to take back France, and might help "sell" a rag-tag fighting force in a mix of British or American and civilian outfits and assorted small arms being French liberators fighting back against demoralized Germans toward the end of the war!)
And, to be honest, while looking around for pictures of WWII French soldiers, I do keep seeing the WWI style great-coats, and believe those might still be correct for early WWII! They seem to be in khaki/mustard green or yellow instead of blue, but at a glance look the same to me otherwise as those on the WWI WA French.