Provence to Florence/Tuscany

Provence is a quite large region. Where in Provence will you be?

You can get a sense of drop-off fees by going to autoeurope.com and putting in your info. In general, the fees are prohibitive.

Depending on your starting point, flying is likely the cheapest and fastest. Check on one of the sites like skyscanner or kayak for options. The common wisdom here is to use those sites for information, but book directly with the airlines.

Well that's a good question...:) Our trip began as Italy only but thought a quick beginning in France (it'll be 20 years since our last visit) might be fun. We don't have a specific location in Provence so are flexible.

It's hard to answer without knowing your starting point in Provence. Most likely renting a car will be the fastest but also the most expensive - may be worth the add'l cost to you or may be prohibitive, only you can answer that. If starting from Nice, the train will be a little slower than driving but not that much and much cheaper and easier - train to Milan, change for Florence, approx 7 hrs. Flying may also be cheaper than driving but a pain in the patoot and may end up taking almost as long, what with getting to and from airports and waiting to board, etc.. Pretty much the same answer applies if coming from the Marseille area - Avignon or Aix are short train rides to Marseille.

Depending upon how you organize your itinerary you may be able to avoid the drop charge by simply returning the car in France after using it for the time you want to visit Florence, ie collect the car upon arrival in Paris (or Nice, etc.), enjoy the car during your time in Provence, drive across the border into northern Italy and Tuscany, then return to Nice (or Paris) to drop the car there.
Most here would advise against taking the vehicle into Florence itself due to the general hassle involved with parking, the risks involved with ZTL's and their associated fines for those unfamiliar with the local traffic restrictions, etc, but having one for touring the countryside is a great way to go.
I'm not aware of any restrictions on simply driving your rental car across the border from France into Italy, but you should verify that with the particular rental car company to avoid any unpleasant surprises...and to ensure that your insurance remains valid.
If you're already committed to an open jaw flight (arriving in France and flying out from Italy) then you would indeed incur a prohibitive one-way drop charge.
Flights are expensive and a train would take most of a day, so driving might be preferable as long as you can sort out the details.

Train travel time between Nice and Florence is reasonable at 7-8 hours but from Marseille or Avignon take 10-11 hours at the best departure times. You usually have to choose between a departure requiring either shorter time or fewer connections; they won't be one and the same. How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it.

Robert's response triggered some further thoughts. We have done an itinerary similar to what he suggests. We flew from the U.S. (San Francisco) to Nice. We stayed a couple of nights, then picked up a car and headed for Italy. There was no problem about doing so, and our AMEX insurance covered us. (Always best to check all of the foregoing, as I do for every trip.).
We spent 12 days touring Tuscany, including 3 nights in Florence, where my brother lives part of the year. Roberto, who often posts here, gave us very useful advice about where to park near my brother's, with explicit driving directions. The garage had a quite reasonable long term rate of 20 euros/24 hours and is outside the ztl's.
We made a big loop through Tuscany, and returned to southern France for another 12 days, ending back at Nice. We returned the car the night before our flight, and stayed at the airport Ibis.