I think a tour would be unlikely, but you can do this yourself without any problems. Managing train transfers is a useful life skill. Do it once and you'll see how easy it is. Just don't load yourself down with heavy luggage.
You'll need to change trains in Milan, but it appears that the schedules usually allow about 30 minutes there, which is plenty of time. You should arrive well before the platform number for your second train is posted. If you want extra time, you can book an itinerary that gives you more time at Milano Centrale.
There are several possible routes from Milan to Avignon. One goes through Switzerland (Brig-Lausanne-Geneva). There should be some nice scenery along that route, but the fare will likely be higher and it requires more transfers. You might prefer the route that sticks closer to the coast and requires only one additional change after Milan, in Nice. If you opted to spend your free time in that city (or taking daily side trips from it), you wouldn't have a transfer there at all. Or you might consider spending a night or two in the Italian town of San Remo, which is much smaller. You might be more comfortable there.
There's also the Thello, but I have no experience with that train.
I'm 65 years old and in the last 3 years I've traveled solo by train and bus through Italy, France, and a bunch of other countries. I am by no means the only not-young female doing that. It's perfectly manageable. The folks at the staffed ticket counters often speak some English, but when I'm not using a ticket machine (those are usually easy), I normally write down my destination, travel date and departure time so there's no confusion. In your case, you may want to buy your tickets now, in order to save (possibly substantially) on the fare. The bargain fares usually come with restrictions; they are typically non-refundable and non-changeable. Therefore you'll want to have your hotel(s) booked before committing to specific trains.
I don't mean to discourage your spending time in Provence. You can certainly go straight through to Avignon on September 1 (if you're free to leave early that day). But that's a long 10- or 11-hour train ride if you don't break up the trip somewhere. Avignon is a city of very manageable size. You could also investigate flying into Marseille or Nice.
