Joffre-class carriers and an Italian response

If war were delayed until 1943, would completion of the Joffre-class carriers force another navy to rush a carrier response?

Yes. The Regia Marina, rather than the Marine Nationale, would be forced to react once France's two Joffre-class carriers were visibly advancing.

The question initially names the Marine Nationale as the navy that might discover it was behind, but France would already possess the Joffre-class program in this scenario. The navy under pressure would instead be the Italian Regia Marina. Once French carriers were laid down and approaching launch, Italy would be unlikely to accept a major new French aviation capability without pursuing something of its own. The precise Italian design remains open; the naval lesson is competitive procurement in the Mediterranean. A delayed war gives visible construction enough time to change the rival navy's priorities.