Advice on itinerary and train options for 3 unscheduled days between Paris and Florence

flying out of locations such as Nice seems to require a return leg to
Paris

Where are you looking for flights? On Google Flights I picked a random day in May and found many flights with only one connection. The 3 fastest (under 3 1/2 hrs) connected in cities other than Paris. Even with the extra time added for getting to the airport, that's still better than 8 hours on a train. I wouldn't be too quick to rule out flying.

So you have 4 days/3 nights for this journey?

You can use the German website Bahn.de to figure out your options (other than spending time in Lyon, etc.); there are several good ones that include Switzerland, as well as one that skips it entirely if you prefer. But I am biased toward Switzerland and it is right on your way.

For all routes, I used Paris as the starting point and Milan as the end; from Milan to Florence after that would be the same options no matter how you reached Milan. Milan to Florence is a journey of 1h 52m on a train with no changes; or there are opportunities to stop in Bologna, Parma, Modena or other towns for a night without a significant detour.

Options from Paris to Milan:

1) There is a direct TGV from Paris to Milan departing at 12:47 and arriving in Milan at 7:40. No good stops on this route as much of it is in a tunnel.

2) Paris to Milan via Torino: this journey is 5.5 hours to Torino, a nice place to spend a night or two. Then stop for a night somewhere else (see the Milan to Florence list above).

3) Routes through Switzerland—-You can travel from Paris directly (no changes, TGV) to Geneva in 3h 11 min; to Lausanne in 3h 40m; to Basel in 3h; to Zurich in 4. Each of these has attractive options for a 2 night stay nearby on on the way.

Heading to Basel, you could stop in Colmar or Strasbourg for 2 nights, then pass through Basel to Spiez, where you can board a direct train to Milan. This one gives you more time in France, and little in Switzerland, but Colmar is a lovely town.

Heading to Zurich, change there for a train to Luzern (1 hour more) and overnight there; then head to Spiez for the direct train to Milan, or take the Gotthard Panorama Express boat/train combo to Lugano and spend one night there.

Heading to Geneva, change for a train to one of the small towns on the lake—-Morges, Vevey, etc.. for 2 nights, then head to Brig to catch the train to MIlan. Same for Lausanne, but it is a nice place to overnight on its own.

Maybe this map of the Swiss rail routes will help you visualize the journey.

https://cdn-doc.myswissalps.com/docs/default-source/rail-network-maps/swisstravelpass.pdf?sfvrsn=7788603a_52

Going to Aix and the Côte d'Azur takes you way off the faster rail routes.
And with 3 nights, I would aim for just one stop. My preferred option is Turin, where there is plenty to see and do in and around the city. Many people here love Lyon too, so that's an option (but Lyon to Florence is still a relatively long day of travel).

The Switzerland suggestion makes sense too, but it will add a little to the travel time and it will be hard to do the country justice in 3 nights.

The amount of time you have would suit most visitors to Lyon or Turin (not both!), I think.

I checked skyscanner.com and found Air France's Hop! budget carrier has two non-stop flights a day from Lyon to Bologna (38 minutes to Florence by train once you get yourself from the Bologna airport to the Bologna Centrale train station). Hop! also has three non-stops a day to Milan Malpensa airport; I see no non-stops to Linate. Malpensa isn't convenient for onward travel to Florence by rail, but you can still get then within 3 to 4 hours. I didn't find any non-stops from Lyon to Pisa.

Even if transportation options from Nice were better, I wouldn't split three nights between Lyon and that area. Lyon is a very interesting city and worth much more than a one-night stopover, and the remaining time would be too short to get a good look at the Riviera. Most Riviera visitors want to see one or two of the hill villages (like Eze and St-Paul-de-Vence) and some coastal spots as well as Nice itself. I wouldn't even choose the Riviera alone with the time you have, given the time you'd spend in transit.

I found no non-stop flights from Nice to Bologna, Pisa or Milan.

I think you are overlooking that it is off-season in Switzerland and in the French resorts you have in mind. This is not a good plan, in terms of maximizing your time. It would be helpful to know if there is a wedding or some other reason for going so far from Paris. I'd suggest art in the direction of Brussels, Antwerp, and Amsterdam. If you've been to Amsterdam, you could finish in Cologne instead of Amsterdam.

Hop! also has three non-stops a day to Milan Malpensa airport; I see
no non-stops to Linate. Malpensa isn't convenient for onward travel to
Florence by rail, but you can still get then within 3 to 4 hours. I
didn't find any non-stops from Lyon to Pisa.

You can also take the train from Lyon to Milan in 4:40, with the added bonus of great view of the Alps.

Hello from Wisconsin,

This is dated information so take it for what it's worth.

We had a trip going the opposite direction. Florence to Paris. There didn't seem to be a reasonable way to do it when considering time involved and price. We eventually went with Ryan Air. And as who have used their service...it was an experience. Not necessarily bad, but you are supposed to print your tickets on size A paper. Ha, Ha, Ha. Try to do that in a Venice B&B.

While we really had time to burn, it was a months long trip. Spending hours, and hours, and hours on a bus or train didn't appeal to us. Connection were poor too. Seems Hannibal had some difficulty getting his pets and luggage from one side of the mountains to the other.

wayne iNWI