Is a day trip from Paris to Avignon, to get a taste of Provence, doable? The train trip is under 3 hours and if I left on one of the earliest trains, I could spend up to 5 hours in Avignon (e.g. a walking tour, a little browsing and have a nice meal) before heading back to Paris. I took the Eurostar to London for a one day excursion from Paris 3 years ago and got a nice shot of that City. I am in Paris for over a month this summer for school and don't have the funds to do a number of side trips that involve staying overnight (I am going to Ireland for five days when classes end.) But I have a few free weekdays and a weekend or two where I could venture a little farther than the towns normally recommended as day trips from Paris.
If you do go, here's a great little restaurant, link below! We ate there a couple of times. It's a 5 minute walk from Les Halles marche and 10 minutes to the Pont d'Avignon
I think the TGV station is out of the historic center, so you'll have to get into town. (15 minute walk to the restauarnt)
Good luck! I'm pretty sure this wouldn't work for me, but it sounds like you'd be up for the challenge and fast pace, providing you can indeed get the early and late train.
EDIT: Agree with Harold's comment below...there are better towns to see could be closer, giving you more time to soak in the city, less time on the train.
A day to Provins, just outside Paris, yes.
A day to Provence, no way.
Paris to Avignon is a long way to go for, frankly, not much. Avignon is only OK. A day in Marseille or Arles or Nimes is much more interesting, if you don't mind the time spent in transit compared with time on the ground (not to mention the money).
If you are looking for long day trips by TGV from Paris, look at Strasbourg, Nancy (an under-visited gem), and especially Lyon (my favorite city in France after Paris). I haven't been to Lille, but a friend enjoyed it more than he had been led to expect.
In my opinion, I think the cost of the train trip and time spent would not be worth it. Avignon is OK, but not a place that I would go out of my way to see. If you could get to a small village in Provence, that might be worth it, or Pont du Gard. I would not do a day trip to see Avignon.
I don't think I would recommend a day trip to Avignon for a taste of Provence. Avignon is a nice place to visit and a good place to base for exploration of some places in Provence but, in my mind, it's not any kind of representation of what people mean when they talk about Provence. It may be less than 3 hrs to get there but for my money would not be worth it for a day trip.