Cinque Terre and South of France?

Yes

I did that last May by train. From CT to Nice, took me seven and half hours (Regional R). I can not find a ES or IC that Saturday.

This may be partially useful. Maybe. I drove round trip Genova - Antibes. I expected scenic vistas on the autostrade. Instead it seemed like one long tunnel for hours and hours. Boring and more boring. I am happy to have had a car for the foothill towns and museums inland from Antibes and in suburban Nice.

I'm not sure why Jeanne hasn't added this, but she PM'ed me to say: "The reason for the combination is I have recently traveled in Tuscany, Florence and that area. I was thinking of spending 3 days in Italy and then possibly going to France." I still don't quite understand the question. After all, it's "possible" to combine a trip to the CT with a trip to anywhere. It reminds me of the old joke "You can't get there from here."

We just got back two weeks ago from this same trip schedule. It was cheaper using our sky miles to get a round trip ticket to NCE. It also was cheaper to rent a car in France and use our AM Exp for the special insurance coverage. It is an easy 1/2 day drive to CT. The last 20 miles into CT is very difficult. You can't have a car in CT. We parked our
car 15.00/day or 70.00/week (euro) in Monterosso. So you really have a choice of an 8 hour train ride or a 1/2 day car ride. If you are looking at 3 nights in CT, with travel you are really only going to get 1 1/2 day in CT. You can fly into GOA, PSA, Milan for FCO but you still will have travel time. We like to hike and stayed 6 nights in CT. There is lots of hiking and wonderful little towns along the coast to visit other than the 5 CT towns. We also spent 9 nights in southern France. We stayed 5 nights at Les Carmes B&B in Provence. It was the highlight of our trip.