Travel from Amalfi, Italy to Marseille France.

Your plan makes sense to me. I'd check flight options from both Naples and Rome at www.skyscanner.com. EasyJet is preferred over RyanAir, if all else is equal, or there may be others in the mix.

Several budget airlines fly direct from Naples to Marseilles. Naples is the closest airport to Amalfi Coast. Use www.momomdo.com. It will pick up a search for the big carriers, like Alitalia and Lufthansa, and budget carriers like Easyjet and Ryan Air, together. I believe Expedia only does the big carriers. When you find flights you like, book directly with the airline's website and not Momondo. As always with budget airlines, mind their baggage allowances, some allow hand luggage and charge extra for checked bags.

You got 3 options direct Rome to Marseilles
Vueling
Alitalia
and Ryanair

I would go with Vueling or Alitalia over Ryanair
You may want to go to Rome before the day of the flight instead of taking a train from Salerno to Rome Airport to catch a flight
depending on the flight schedule.
Try booking directly with the airline Vueling.com or Alitalia.com.
I have used Expedia many times many years without drama as well.

Volotea flies from Naples to Marseille. We flew on them from Bari,Puglia to Palermo, Sicily in October. Their non stop flight saved us many extra hours of flying Alitalia via Rome. Check in was prompt and easy, flight was on time. We paid extra for early seat selection.
No problems at all. They connect smaller airports in Europe.
Book directly with Volotea, no middle men like Expedia needed. Volotea sent us lots of updates and we got our boarding passes right when we booked our flight.

It is a lot further, especially time wise since you have to go to Rome and then to the airport. So it makes more sense to fly out of Naples. I don't know where you are since Amalfi is an area and not a place. It could be more convenient to go to Sorrento and to the Naples airport from there.

Volotea flys Naples to Marseille flight time 1:50

Take the ferry to Salerno, train to Napoli Centrale. Alibus to the airport.

This would all be time dependent.

Other option ferry to Salerno, train to Rome there should be more flights from Rome.

Or you could take the train. Two easy changes, in Milano Centrale (41 minutes) and Nice Ville (23 minutes). Frecciarossa to Milano, Thello to Nice, then TER.

It does take between 12 and 13 hours. Or you could break it up.

You could take the ferry from Amalfi to Sorrento and then hop the airport shuttle bus that takes just over an hour to get to the airport. I would not bother traveling all the way to Rome since there are a number of flights from Naples.