Tuscany in June

Lucca is a cute little town for a day trip, and it was a very pleasant and unique experience to rent a bike and ride along the top of the walls.

Pisa is the kind of thing you can do in two hours. Look at the tower, look around the cemetery, look at the ceiling of the church, and then gawk at the floods of tourists taking silly pictures and hit the road.

My favorite experiences from Tuscany were, unfortunately, not covered in Rick Steve's Italy book (that may have changed in the last few years). We rented a car and drove through Chianti, stopping at a few small towns to eat and have a look at a castle or a vineyard here or there. The countryside was beautiful and the people were much friendlier than in Venice or Florence.

My favorite experience was going to this unique butcher, sampling lardo, and then sitting up on a hill overlooking Panzano drinking Chianti Classico wine and eating about a half pound of the best salami I've ever had.
Here's the butcher shop on Tripadvisor,
And here he is on a low quality clip of Anthony Bourdain's old show.

Second Lucca. Also got very enthused about Siena on a recent trip.

If you only have 6 nights and your starting point is Paris, I would definitely fly from there to Florence. Even with high-speed rail, the train trip would eat up more time than I'd want to spend.

In Italy do you want to rent a car, or travel around by bus? Since you'll be recovering from taking students around, do you mostly want to stay in one place? I could imagine myself choosing a nice quiet pensione or agriturismo and mostly just chilling out there, with maybe a day trip to a neighboring town or two.

As for a beach, well, as you know, Tuscany is mostly known for its inland towns, vineyards etc. Although Cinque Terre is on the coast, personally I wouldn't choose it. Others on this forum may know more about the coastal areas. I haven't been there, but this website has lots of information: https://www.discovertuscany.com/what-to-do-in-tuscany/top-beaches-in-tuscany.html

Having been a woman alone on an Italian beach (Tarquinia, many years ago), I'll note that you may want to attach yourself to an all-female group or a mom with kids. Attitudes may have changed, but there has been an unspoken assumption in Italy that a woman alone in a place like the beach is looking to, ahem, meet new friends.

Easyjet has a few flights to Pisa a day from Paris Orly 1H35m.

There are two beach towns close to Pisa, Viareggio 15 min. and Forte di Marmi 38min.
Both by train.

Pisa-Lucca will take 28 min train ride and there's a bus that will take you to Barga in about 30m.
For a great day trip from Lucca.

And from Lucca you're a little over an hour to Florence and the Cinque Terre.

Edit: Forgot to add, another day trip from Lucca is Borgo Mazzano, either by bus or train, to see"Devils Bridge".