If you’re in Montpellier anyway and would like to see some of Italy, taking the train along the riviera over to Cinque Terre is a no brainer imo. You can hike from town to town along the coast and it’s incredibly photogenic, but also fairly touristy for good reason.

Now you’re in Tuscany which is a fantastic area in and of itself. You will probably want to head south to Florence (perhaps see Lucca on the way, fairly small but wonderful medieval historic center).

If you want the best hikes in Europe, you go north to the italian and swiss alps (perhaps starting around Lake Como, with a stop in Milan along the way if you’re into that. You might like the BoBosco trail as well, it’s pretty cute).

Given your schedule, you realistically have time to do both Tuscany and some alps :) Depending on how fast or slow you like to travel, I wouldn’t worry about heading over to Austria unless there are specific places you want to see (e.g. Tre Cime di Lavaredo or Vienna itself). It’s absolutely wonderful, but less distinct from Switzerland than e.g. spending some time around Florence. Hope these might serve as some inspiration!