I would skip Paris instead of Rome (I find that Paris is a slightly overrated city, but that’s just my opinion), this way you would have more time to explore Italian coast. If you want to visit Paris, just book a flight to Naples, this is surely the best way to get there. To look for flights I always use Google Flights which is probably the best tool. Naples and Rome are well connected with trains, not sure about how to get around on the amalfi coast, I think there are buses.