Help with basic Itinerary

No Normandy? No Mont St Michel? No Chateaux of the Loire Valley??
You didn't say if you've been to France before - maybe you've already been there, done those?
If you have not, I'd gladly trade several of your places for them. Other thoughts...
Your trip is short - how many full days do you really have? Not nights, but full days, not including your arrival in Europe or departure days. Don't count your jet-lagged arrival day, that's not really a usable day (you'll probably be a zombie).
Tasting champagne in Reims would be nice, but I'm not sure I'd spend a precious day on that. Regardless, I don't see any reason to go on a "tour" for this.
One challenge you have is trying to do Paris (which is in the north) combined places in the south (Arles, Avignon, Burgundy, etc.), and that travel time will eat up a bit.
Tastes vary, but the three items I listed (Normandy, Mont St Michel, Chateaux of the Loire Valley) were among our very favorite places in many trips to Europe, and I'd consider them among the "cant miss" places in France.

In planning your trip for May, take into account public holidays: May 1 and May 8, and then later in the month, Ascension Day, May 25. If you are going to travel by train on these long weekends, make sure to get your tickets early because the cheap tickets will sell out quickly.

I don't think you have time to go to Nice. Depending on what kind of food and wine you like, you could end your trip in Lyon instead of Provence. If you choose Provence, I would stay in Avignon rather than Arles for food. I like Arles as a base but our RS book indicated that restaurants were not that great there and that was our experience. We preferred restaurants in Vaison and Avignon over those in Arles (we had 8 nights between the 3).

Good luck with your planning

Thanks for the thoughts. We have never been to France, we will have 10 days total.
Since we will not be using a car, and don't have ample time to deal with local transport, we left off the Loire and Normandy. From the guidebook it sounded like these were best with a car. Also, based on our interests we were okay leaving these areas out, other than Mont St-Michel but I'm not sure how to fit that in.

Thanks for the information on the holidays, we do plan on traveling on the 8th so we will book early. If we flew into/out of Paris, and went directly to Avignon, would it make sense to add the 'extra' day in Avignon or Beaune or add a one night stay in Lyon? Or does it make most sense to just cut out Provence?

With only 11 nights I would drop Paris back to five. Then choose 2 destinations (from Burgundy, Provence, Côte d'Azur) for 3 nights each.
Lyon for flight departures from Burgundy.
Marseille for flight departures from Provence.
Nice for flight departures from Côte d'Azur.

If you are ending your trip in the Arles/Avignon area, fly out of Marseille (MRS). If you're ending in Lyon, fly out of Lyon (LYS). There's no need to go to Nice just to use the airport, and I wouldn't waste time getting there on such a short trip (Marseille to Nice is 3 hours) only to spend a half day.

Do be sure to look other sources besides Rick Steves before deciding where you want to go. Rick only covers parts of the country (by design).

Based on your description of what you are interested in, I would train immediately to Lyon (2 nights), then spend 3 nights in Beaune, then 6 nights in Paris. I think (based on your interests), you will find Provence without a car disappointing (and going to Nice will certainly be a waste of time for 1 day and a flight). With this itinerary you are putting yourself in outstanding food/wine places, minimizing travel time, and experiencing big city, medium-sized city, and rurals all on easy train travel. I agree that if you want to avoid renting a car, sticking to the east is the way to go. Beaune is a lovely place to experience the countryside by bike.

-Matt

Re Reims and "...Is this easy to do on our own or should we go through an organized tour?" Getting to Reims and back and touring on your own is a piece of cake. It can be done as a day trip, albeit a looong one. If you go there, you might want to consider a one night stay as Reims has a lot to offer other than Champaign tasting. Lots of folks on the forum have done it -- some one way and some the other -- so getting the details of how to do it will be readily available.

Day 7-8 (2 nights) Train to Burgundy - Dijon or Beaune. We really want to spend a day bicycling around to vineyards. Would Beaune be the best option?

The reality is this: get up, finish packing and eat breakfast, take metro or walk to train station in time to find your track, arrive in Dijon/Beaune with your luggage and make way to hotel from the station, leave your bags at the front desk because your room isn't ready until 3pm. Eat lunch. Now you can resume sightseeing.

The point is you don't have 2 days in Burgundy, you have an afternoon and then a full day, and you're likely to find your energy a bit sapped that 1st afternoon.

I would suggest instead dropping one destination and staying 3 or 4 days in Burgundy. But of course travel preferences differ and maybe you'd like to at least set foot in all these places this trip.

For a compact trip, it looks like you've nailed it, with the exception of the unnecessary and short hop to Nice. The rest are fairly short trips on the same rail line south. However, instead of going to Nice, you could spend the day visiting Cassis, the Calanques, and go one stop further east on the local train to Bandol, since wine seems to be a very strong interest.

So that gives you Champagne, Bourgogne, Rhone--either northern region if you stayed in Lyon, or southern region if you stayed closer to Provence, assuming you had Chateauneuf du Pape in mind. Finally, a quick Bandol in 11 days. Not bad. Cassis has wine but the view is better.