Others will be able to give you much better answers to this than I can, but a good place to start mi

We are going to be in the area In mid October travelling from Rome to Paris and would like to stop at one of these areas. I have been to Florence before and LOVED it. I would like to visit a town/towns inbetween ROme and Paris that are smaller, walkable, relaxing, but still have a lot to do/restaurants etc. We will be travelling by train but are willing to rent a car for a few days. Looking to spend about 4 days in one of the Riveria areas.
Others will be able to give you much better answers to this than I can, but a good place to start might be to look at the train routes and decide what would be convenient and enjoyable for you. Do you want to stay in a different disneyland hotel paris place each of four nights, or stay in one place all 4 nights and day trip?
Sorrento and Portofino would not be on your way to Paris. And i don't recommend Monaco... Seriously expensive and not as interesting to visit as it sounds. Nice is a lovely option; be aware that it is a city, not a small town, but you could easily day trip from there to the other coastal French towns. Of course, Oct won't be beach weather, but lovely weather for walking and relaxing.
Well Sorrento is south of Rome but the positive would be warmer weather. I would not stay in Monaco - overpriced. disneyland hotel paris Nice is nice - I really like Nice - lots to do, many inexpensive day trip options using the local bus or you could rent a car. Near Portofino is Santa Maria Liguere (SML) - larger town, less chi-chi so some more moderately priced options. My choice would be either Nice or SML unless you want to head south to the Amalfi coast / Sorrento area.
We stayed at Villefranche-sur-Mer a few years ago at Hotel Welcome and loved it. You can drive up into the hills behind the town, tour Nice, etc. easily from there. You can even visit Monaco. Good base for a stay.