The Caporetto gap is fine in WWI. In 1939, however, it was deep in Italian territory, the border having been moved rather farther East. A Germany that has defeated France first, then Yugoslavia, could still force the pass at Medvedje Brdo, then advance for some 75 kms in the narrow Idrijca valley, thus reaching the upper Isonzo valley, and Caporetto (Kobarid). Not so easy and quick, and the Italians would see them coming.
That said, personally I believe that if the French-British-Italian-Yugoslavian alliance is crazy enough to let the Germans take them out one by one, the Germans can force the Eastern Alpine passes and valleys, in summer. The butcher bill will be high, but with a combination of small paratroop drops, sustained air superiority, and sheer firepower, I think they can.
That done, they are still very very far from Rome.
And as pointed above, if Mussolini has chosen the French side of the fence, then the obvious move is to deploy most of his strength in the Western Alps. Even if he doesn't attack, it's entirely likely the Germans flounder somewhere in France, because of the altered balances of forces. If he does attack while the Germans are committing to their Western offensive, I think Germany gets what they deserve straight away. Not by any Allied lightning advance, but simply because the Germans are stopped - and staying put, for them, is defeat.