If we replace the Zero with a different contemporary design that has similar combat capability but a very different design approach, we can then discuss weather it would change much.
Take for example the D520.
Had the IJN been using the D520 in its navalized form, the superior training of IJN pilots would still allow them to overcome allied air strength in all the initial campaigns. Having used it in China, they would have developed tactics to suit their fighter and woul probably score the same massive kill/loss rates against allied fighters. Thelack of range would not have been a decisive facto. It would force the carriers to get a bit closer to Pearl, for example, but that wouldn't change OTL events.
The main difference would come in the Solomons campaign were the lack of range of the D520 would mean there would be no long range missions. This would reduce pressure on the US forces, but also reduce IJN fighter losses.
So as along as they have a decent fighter, their superior training will give them the same six months of superiority.
I've looked at the French flight line for aircraft that they could have used for aircraft carrier service if they had been able to launch outfit and commission the two through deck cruisers Joffre and Painlevé they intended to build.
It is scarce pickings.
a. Dewoitine D.372 biplane fighter
b. Levasseur PL.10 biplane scout/recon/observer aircraft
c. Levasseur PL.7 biplane bomber
Of the land based offerings that are available circa 1940, that could be possibly navalized, because of the ruggedness needed in the airframe and the simplicity to maintain and resistance to salt water necessary, again the pickings are slim.
d. Morane Saulnier MN 406 with a more powerful engine that boosts it into a competitive position, possibly by using a Hispano Suiza HS 12Y-31 or later model engine. It would be very much like a Grumman Wildcat in performance if not in sturdiness and survivability. One advantage it would have is the 20 mm Hispano Suiza HS 404 cannon.
e. Optimized as a dive bomber... Loire-Nieuport LN.401 which was purpose designed. My complaint against this aircraft is that it can only dive shallow as its tail control is very suspect as it goes in a steep 60 degree or greater dive. It probably is better as a scout recon bird. It could in a pinch be used as a backup fighter like the Douglas Dauntless was used in USN service.
f. There is no replacement for the Levasseur PL.7. The best candidate, the MB 151 would need too much reworking and the only other suitable bird, the Bloch MB-480 is a twin engine aircraft too large to embark as a deck landing aircraft on any proposed French construction. It would fit an Akagi however.