If they already control Germany, making it into a federation won't increase their political power anywhere.
You know what nationalism is, right? Nationalism wants to build a nation-state. A nation-state is the literal opposite of a federation of multiple nations, especially not a federation where your country is inferior in population and is thus in danger of being assimilated.
That's why no serious Polish nationalist leaders wanted to restore the Commonwealth, even if it's a major source or pride for them, nor did they back the Intermarium project.
Nobody ever really questions France being one of the major powers in Europe, so that point is moot tbh.
And besides, France did not have a large fascist/monarchist contingent during this period, and extreme nationalism would be discredited by the Nazis anyway.
You know what would be nice? Stating the reasons for allying someone in the actual TL rather than withholding them until someone asks.
In my opinion, Greece is a lot more strategically and patriotically important to Italy than Hungary, Yugoslavia or Austria, and since the French would have a very tough time defending it in an invasion, I see no reason why Italy wouldn't want to just take it from the French and give them the middle finger. France is still tired from WW2, after all, while Italy didn't fight.