Yeah, I agree. If Germany fails to take Paris, even if the Italians end up taking Paris it will definitely slow things down for the Axis. Germany won’t have as much money to spend on Sealion or even Barbarossa. Since Italy has to commit resources to taking Paris, that will set them back in the Med and Africa. Plus, if Sealion fails or just doesn’t happen because Germany doesn’t think they can do it, the Brits could really take advantage of the situation in Africa and make things rough for the Italians, even with the extra French money. I’m not saying the Axis couldn’t still win the war, it will just be harder to do.
Of course, if France doesn’t fall to Germany G1, Italy does have the option of ignoring Paris and moving on with their Med operations. Problem with this strategy is it leaves an enemy force right there on both Axis country’s doorstep. Not sure if Paris could survive a second German attack but at the very least, it would take even more German resources and Sealion would be just about out of the picture. Unless Germany went ahead with Sealion without taking Paris first. I wonder if that could work.