Leaving on a cruise from Savona, Italy - fly to Paris then ?????

Is there a reason why you don't want to fly to Milan? From there you could take a train via Genoa.

If you flew to Paris and took the train, the route that goes through Lyon, Marseilles, and Cannes is the one that will bring you along the coast toward Savona. It looks like Ventimiglia is the nearest station so you would take a taxi from there.

When is this trip? Nonstop flights between Paris and Nice typically cost US $60 if booked ahead. I see many such prices available for this September and October. You can fly from Paris to Milan or Genoa/Genova for similar rates. See www.skyscanner.com.

A TGV train will often be more expensive, with Paris-Nice full fare about $125 in 2nd class, unless reserved well ahead for a discount.

Looking Up Train Schedules and Routes Online gives you the Deutsche Bahn train schedule link and tips for using it.

We have been able to book a round trip flight, New Orleans to Heathrow, on our air miles. We have also brought transfers from Genoa Airport to the ship. Now we need to book Heathrow to Genoa, then Dubai to Heathrow. I have never been to Europe, don't know anything about local airlines. We gave ourselves a one day layover in the way to Genoa, and two days in London on the way home.

Trip is from late November to mid December.

Try using one of Europe's budget airlines - https://www.ricksteves.com/travel-tips/transportation/budget-flights

Be sure to buy the required ticket(s) for your bag(s) if you fly a budget airline. I flew Air Berlin from Berlin to Luxembourg and they were very surprised that I showed up with luggage. I had to stand in another line for an hour to buy my bag a 50 euro ticket. Other than this problem, the trip was quite good.

On the other hand, high speed train from Paris to Milan start at as little as 59 euros and takes 7.5 hours. https://www.eurail.com/en/europe-by-train/high-speed-trains/tgv
You could complete your trip on a local train.

Also, avoid traveling thru Spain. News stories in Europe this past week show massive lines at Spanish airports due to Spanish airport workers protesting & working less than usual.

Thanks for the great tips. Things that are so normal to the local folks are totally unknown to the tourists!