Like Wiking, I don't see a bilateral initiative as plausible. However, I could see both becoming de facto allies if Italy chooses them both as junior partners.
My immediate thought was that this is unlikely given Italy's OTL support of Hungarian irredentism and hostility to the Little Entente. But there were signs that the Stresa Front (if it could have lasted, which IMO is unlikely) could change that:
"Neither the French nor the Italians wished to make Stresa too pointedly anti-German—hopes for a rapprochement with Berlin restrained Laval's interest in an alliance with Rome—but wanted to approach the German problem from a position of strength. Still, already after Laval's January visit to Rome, the Italian high command had begun to press Paris for the conclusion of a military convention. After Stresa an air agreement was negotiated, and in late June talks between Gamelin and Marshal Pietro Badoglio established the foundations for military cooperation in wartime. Notably, a French expeditionary force in Italy would act as a liaison with Yugoslav and Czechoslovak armies, and some Italian air squadrons might be based in Czechoslovakia. General Gamelin kept the chiefs of staff of the Little Entente informed, and reported that Benes and General Syrovy attached particular importance to the presence of a French corps operating on the right flank of the Italian army. Such an arrangement would promise the quickest assistance to Czechoslovakia.
"Although worried by the possibility of Hungarian and Bulgarian rearmament, Benes and Krofta viewed Stresa as indicative of a definite and welcome change of Italian policy toward France and the Danubian region. In Benes's thinking the necessary sequel to Stresa was a speedy conclusion of accords with Russia, which would result in the emergence of a "great security bloc." By contrast, Beck, irritated that Poland had not been associated with the conference, viewed Stresa as an attempt to return to a great powers consortium. He was also skeptical about the alleged solidarity of the three, for "each of the powers only thinks how to reach a separate accord with Germany." The immediate future showed that his estimate was more realistic than that of Benes..."
https://books.google.com/books?id=zwgABAAAQBAJ&pg=PA394