The unclear nature of the divergence introduces a lot of uncertainty, so I'm leaning on the "No Fall of France" aspect.
By 1940, both Spain and Portugal are under Fascist or Fascist leaning regimes which have much in common with Italy. Libya, and East Africa in the form of modern Ethiopia, Somalia, and Eritrea are already colonies. There's a lot of pent up Anti-Anglo French/Pro Axis within the Middle East too, as evidenced by the Iraqi Uprising of 1941, the situation within Iran, Egypt and Palestine (The Grand Mufti has already long since established a dialogue with European Fascists). That's a pretty firm basis for an Italian sphere of influence and direct control already, and presuming trends in the Third World are like that of OTL it'll only grow.
Presumably, the Anglo-French will spend 1940-1942 battering themselves against the Germans until Stalin comes West with an unbloodied Red Army in May of 1942. Depending on the actions the Germans, and to a lesser extent the Soviets and Anglo-French themselves take, the latter will meet the former either on the Oder, the Elbe or possibly the Wesser; it mainly depends on how the Germans respond. The Anglo-French will be exhausted and facing a much, much more powerful Soviet Union without even the benefit of American support from IOTL. What remains of their energies will be utterly focused on this contest, leaving little to spare to confront Italy and, really, why would they? It makes more sense to be conciliatory to Italy (and Japan!) here then hostile. Certainly the instincts of the Anglo-French Governments historically was to attempt to keep Italy aboard in the 1930s anyway historically.
As decolonization, Italy emerges a prime patron for most of the Middle East. The Anglo-French are hated and will be more so if they still try to setup Israel under American pressure, while Soviet Communism will remain a turnoff to many. Italy thus stands as an agreeable patron ideologically while also being strong to be of value but not too strong that it can be as overbearing as the Soviets and United States were historically. This also extends into Africa; Apartheid South Africa can find itself with a ready ally in the form of Fascist Italy, same for Rhodesia. Portugal will benefit immensely in holding its colonies with the support of Italy. Imperial Japan will also find Italy agreeable in the context of the Anti Comintern Pact, while perhaps Hungary, Bulgaria, and Greece will likewise gravitate into its spheres as the threat of the Soviets also increases. Yugoslavia is, however, an open question mark. Argentina, Paraguay and others might also see a high degree of Italian influence, both due to the resident Italian populations and the nature of those regimes.