Germany was not inspired by the colonial empires of its contemporary European powers so much as it was by the settlement colonies of the West, those of Britain particularly. There, Indigenous populations had been marginalized, first politically subordinate and then reduced sharply in numbers, before their territories were seized and eventually repopulated by migrants dispatched by the colonizing powers. For the Nazis, the
Mississippi prefigured the Volga in their preferred future, each river becoming a riverine corridor in the heart of a newly settled territory.
Was it possible that Vichy France and Italy might do the same sorts of things in their spheres that Nazi Germany did in it? I'd argue that if Nazi Germany has established a precedent for the genocidal recolonization of Europe, it will make like acts more thinkable on the parts of its satellites. We could turn to the bloody conquest of Algeria by France in the 19th century, to the much more recent but comparably bloody Italian conquests of Libya then Ethiopia in the 20th century, and note the potential for Generalplan Ost-type plans in those territories by their rulers. An Italy that engaged in indiscriminate reprisals against Slovenes, for instance, and had prominent members of its government imagine even Slovenes' extermination, might well not flinch at the idea of ending the Arab problem in Libya.