Trip by rail from Nantes to a place on the southern French Coast, with a stop in Italy.

I would definitely fly back to Paris from Genoa. There are 3 flights a day.
It is going to be exhausting all the train trips hours on the train for two weeks and checkin checkout of hotels.
You might just stop in bigger towns like Toulouse and Nice and take day trips to the small towns to cut down the hotels at least.

I would suggest resolving the round-trip aspect by not making this a round trip. Fly home from Italy, probably Milan.

Yes, you have 9, maybe 10 places in two weeks. Even a 3 week trip seems rushed. If I may read between the lines, seems like the following stops are important. Nantes (friend), Montauban (mom's home town), Montpellier (college days), Vence (relax), Genoa (Italy bucket list). In addition to those, add a first night in Paris and a last night in Milan. So I'll put this on the table;
Paris 1 night
Nantes 2 nights
Montauban 3 nights
Montpellier 2 nights
Vence 3 nights
Genoa 2 nights
Milan 1 night
That is 14 nights plus the over night on the way, add 1 more night in there at wherever you choose and that is a Friday night to Sunday 2 week holiday.

Nantes to Montauban you can fit in a 4 hour stopover in Bordeaux, time enough for a leisurely French lunch and a bottle or two of wine, I hear it is pretty good in that neck of the woods.
Look at renting a car for 2 days in Montauban to explore. Then Montpellier, Vence, Genoa, and finally Milan.

Cheapest flights home are a direct to JFK then a connection to Boston from there. Sister can get a direct train back to Basel in 4 hours.

9 places in 14 days is quite a bit. That's a lot of travel time and moving around. To make it a bit easier I would fly open jaw landing in France and flying home from Italy. Any particular reason for Genoa? It's not the best place to go in Italy. I'm honestly not sure how to make this trip better - it's a bit random as far as the locations go except for the family connections. These are all great places but she won't be able to spend much time in any of them.

Any particular reason for Genoa? It's not the best place to go in Italy.

Come on now, the point of any person's own planned trip is not to only go to where a stranger thinks is the best place.

Thank you all for your suggestions and advice. You've been most helpful. I only picked Genoa because it was closest by rail to Vence. My sisters will not have a car. You have helped me by making me see that the trip will be rushed as I've suggested it, all those train trips and stops. That is why I posted on this forum, to get some sense of what makes sense. So, thank you! I will take all your advice and replan the trip.

Sam, why do you suggest three nights in Vence? Is it that good there?

Just a guess, really. It seemed like a pleasant place to chill for a few days. To be honest, first thought was that you misspelled Venice. Then I read this.
https://www.telegraph.co.uk/travel/destinations/europe/france/provence/articles/Richard-Madeleys-Vence-My-Kind-of-Town/

Thank you, Sam, for the article link. Can't wait to read it. And thank you, andrew.reis, for your suggestion over Genoa. I will check it out.

If any stops on the way are only there for the purpose of breaking up a long train ride, then another flight may also be the answer. For instance, Easy Jet flies nonstop from Toulouse to Nice a couple of days per week or completing the train ride in one day takes 7-8 hours (which would not be too long for me). Volotea flies from Toulouse to Pisa once or twice a week in high season. Both of those airlines fly from Toulouse to Venice, etc. So I think she should prioritize her destinations first and then can probably find transportation to fit.

Thanks for your input, Laura. Yes, the more frequent stops are to avoid long train rides for my sister and not eat up days traveling, especially since I've now found out that the sister who is accompanying her can only do a 12-day trip total (and the sister this trip is for would not be comfortable traveling extra days on her own). If one were to travel very lightly, like my Dad did with just one small shoulder bag, then the more frequent traveling could be fun, with a minimum stay of two nights in each place. Again, the suggestions from this forum have been great...helping me rethink and modify the outline I started with. My sister just wants to go and is relying on me to plan it out. The good thing is that both my sisters speak French fluently.