Joan,
Doesn't look like heaven for hotels!
You might want to have a look at the tourist office's web page which lists all hotels in town (some three 3-stars) and also some outside the town.
Just click onto 'Hébergement' and scroll down the page. When you click in the hotels' names, you will most probably get detailled information.
Hope this helps for a start, if you really need to overnight right there.
http://www.chalon-sur-saone.net/Oh, the Hostellerie de Bellecroix (a Châteaux de France hotel, also Relais de Silence) in Chagny does look rather inviting.

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