Would Italy actually build a carrier?

Would Italy build an aircraft carrier in this scenario?

Yes, if France built a modern carrier; French construction would create the political pressure Mussolini could not ignore.

Mussolini could disregard the old French carrier Bearn because it posed a limited modern challenge. A Joffre-type carrier would create pressure for an Italian answer. Italian construction in this scenario therefore depends strongly on France fielding a credible new carrier.