Having a difficult time finding accommodations in January in Provence

Rick lists only a tiny fraction of the lodgings in Provence. You may get more helpful suggestions if you provide a per-night budget in euros, tell us the number of people you need to accommodate, and list the towns you hope to visit.

In the meantime, you might take a look at booking.com, where the reviews are all submitted by people who have actually stayed in the property in question and you can set filters for the features most important to you.

In Lyon u could try a chain French hotels, not fancy but central and squeaky clean walk to train station also.
Ie. campanile hotel chain

Any Ibis Hotels if you can't locally owned. Rick Steves has said somewhere he likes that chain

Small touristy towns in France are often pretty dead in winter; hotels close, restaurants close -- the economy of small quaint towns is tourist driven. We once had great trouble finding a place to sleep in the south of France near Oradur sur Glen in early May -- I had a list of 6 hotels and every one of them was closed and I felt lucky to finally stumble on a kind of terrible place that had rooms. I'd pick the places you hope to stay and look at the hotels on trip advisor in those towns -- you have their ratings etc and you can contact those that appeal to you to see if they are open. You may also find that other things you want to visit in the area are closed.

In your shoes I would confine my search to Avignon, Arles, and Nimes, and if necessary consult other sources for recommendations.

That time of year you will want to be based in a city where there are plenty of choices of things to do in bad weather.

Thanks to each of you who took the time to respond. I LOVE the Forum group! Thanks, Shay

Trip Advisor has Numerous listings for the area that you want to visit.
Mike

Per the above, try also the larger towns and cities, as you'll also find shops and restaurants closed in these smaller villages. On top of that, many business owners who do not close the entire winter close just in November or January, to take their holidays somewhere sunnier and warmer.