I think this relates not to 1939 (when Mussolini was deepening his alliance with Germany and joining in the territorial predation with his seizure of Albania) but to the moment in 1935 when Britain, France and Italy briefly presented a common front against nazi threats to the 1919 peace settlement.

Mussolini had earlier (July 1934) moved troops to the northern frontier to ward off a threatened nazi seizure of Austria, and all three powers were alarmed by Germany's repudiation of the military provisions of the Treaty of Versailles (March 1935). French efforts to extend a multilateral guarantee of Germany's western frontiers to the east had meanwhile (September 1934) foundered in the face of German and Polish rejection.

The April 1935 meeting at Stresa (northern Italy) between prime ministers MacDonald, Laval and Mussolini issued a joint statement committing their three countries to maintain Austrian independence, seek arms limitation and pursue the recent Anglo-French proposal for a common air defence guarantee against aggression. The final declaration stated:

The three Powers, the object of whose policy is the collective maintenance of peace within the framework of the League of Nations, find themselves in complete agreement in opposing, by all practical means, any unilateral repudiation of treaties which may endanger the peace of Europe, and will act in close and cordial collaboration for this purpose.

The arrangement started coming unstuck only two months later when Britain concluded its own agreement with Germany limiting the latter's naval strength but in excess of the Versailles ceiling. Both the French and Italian governments were angered at having been left out of the discussions and now facing greater German strength than previously.

The final undoing followed Mussolini's October 1935 attack on Ethiopia: both Laval and British foreign secretary Hoare lost office after secretly proposing to buy Italy off with Ethiopian territory, and the two powers fell into line behind general international condemnation of the invasion. Italy went on to make its own deal with Germany, formalised in the 1936 Axis accord.

So I think it's this episode and particularly the naval agreement controversy that the question refers to. The "Stresa front" was never as strong as it seemed to be, the accord itself being hedged in diplomatic language committing the participants to little specific action. But even if the naval deal hadn't finished it off, the Ethiopia war (planned by Mussolini months before the conference) would have done the job six months later.