I think what you need is no Operation Husky, no invasion of Italy etc. But even before that you need to prevent the rapid disintegration of Fascist Italy. Which probably means delaying the Italian entry into the war for a while.
In fact it might be better to just avoid the war at all.
So maybe after the war the Fascist regime tumbles on for a few more years then is overthrown in revolution for whatever reason, ether due to decay or from having joined the war late(ish) then backing out and signing a negotiated peace. Or whatever.
The Italian Communists try to take power during the revolution. And the entire mess just spirals down into civil war from there with the USSR and NATO backing their respective sides with the Fascist remnant as the third wheel.
With the west to tired to directly try to solve the problem with force an agreement for a partitioned Italy is agreed, with communist north and monarchic South.
France would be the one most against having a communist neighbor. But if you tie them down enough in Algeria, and the left in France being highly against war, maybe throw in some failed interventions, then you might be able to get the French to give up as well.
Not very plausible i suppose. But its probably as plausible as having the USSR take over North Italy by force in WW2.
