Accommodations on the fly in Baune and Nice

For Beaune, you could make cancellable reservation on booking.com (we stayed at Beaune Hôtel, good parking) and change it as needed. Make sure you know how far ahead you need to cancel -- some are 1 day, some are more. FYI, driving/parking in Lyon can be stressful!

You'll definitely need reservations for Paris during October but outside of Paris it becomes much easier in the fall to find accommodations with little advance planning.

If you're flexible on where you wish to stay, then you should be in pretty good shape traveling without reservations, though Nice might be a bit tougher than other locations.

If you have your heart fixed on a particular spot, it's best to reserve it ahead of time.

October is a bridge month in Nice, and towards the end of the month the tourist traffic drops off considerably. But if you have a cancellable reservation you can remain flexible, as others noted. You might also consider picking up a stay in western Provence as you head south.

Spend some time Googling to check for special events in the areas you plan to visit. If you're clear on those, I think the area around Nice will probably be fine. If you do a preliminary check for rooms on a site like booking.com 48 hours ahead of time, you should have a warning if you've overlooked something significant, because there will be few rooms available and the rates will be far higher than expected.

I used to make a list of potential places, then call the morning before I arrived. I almost always got my first choice. My French friend uses trip adviser to book on the fly. If you have a smart phone, that seems to be a fairly popular approach in Europe. You can see what's available, check reviews, then book yourself.

I didn't have trouble finding openings along the Riviera in late September, though I'd suggest Antibes (or Juan les Pins next to it).

Also you can put the Airbnb app on your phone and look for a place with them.

Thanks to everyone for your help and advice!