While we have done many wineries here on the west coast, Spain, and Burgundy, only Bordeaux region offers tours to a couple of the only seven premier grand crus: Mouton Rothschild and Margaux, Cadogan guide was very helpful. The ride up the Gironde Estuary and back down along the river also took us past the stunning dovecote of Latour (no tours available). Cite du Vin was not yet open and not of interest to us in the city, but with advance ticketing, these two premier crus, including the Rothschild art museum onsite were well worth a long day. Can't speak to convenience of getting to Nice from there, we TGVd from Paris, picking up car in Bordeaux, driving east before heading south to Provence. We would revisit Bordeaux before Dijon/Beaune anyday IMHO -- chacun son gout non?

I can’t comment on travel logistics but two friends were in Burgundy recently. One stayed in the darling town of Beaune and followed the Rick Steves guidebook suggestion of renting bikes and following a wine route. The other stayed in Dijon and took a fantastic tour to a winery.

Both places are on my list!

That said, I have recently taken the TGV from Paris to Avignon and it was quick and easy.

A honeymoon in France sounds amazing!

Not a wine tour exactly, and I realize it's not exactly what you are asking for, but you could consider taking the train from Paris to Reims and touring a champagne cellar. There are some that are within walking distance of the train station - and the high-speed train from Paris is short enough you could do it as a day trip. Reims is a charming city - beautiful cathedral and compact old town, very walkable. Some great dining options, too.

It wouldn't waste the time of checking in and out of a hotel, etc. mentioned above. Could be added on to your time in Paris, if you can make time for an extra day.

We enjoyed touring Taittinger cellars - which is not too far from the Visitor's Center in Reims (walkable). Fascinating natural cellars - and free glass of champagne at the end. Be sure to bring a sweater - the further down into the cellars you go, the chillier it gets.

It's easy enough to do on your own, but if you are more comfortable with a formal tour, there are options. From Paris: Reims and Champagne Tasting Full-Day Tour | GetYourGuide

Happy Honeymoon!