What is the best way to get to Paris from the port of Citivavecchia?
It all depends upon your definition of "best." If you want convenience and aren't worried about expense, take a private shuttle (over €100) from Civitavecchia to either Fiumicino or Ciampino and fly to Paris. Or take a train to Rome for a few euros and either a train or bus to the airport of your choice.
For budget airlines, your best choices are Fiumicino-CDG on Vueling or Ciampino-Orly on easyJet. Ryanair flies Ciampino-Beauvais, but Beauvais is a long way from Paris.
Or spend a few hours in Rome after your ship docks and take the direct night train from Rome to Paris. No hotel bill and a relaxing ride.