A good site to consider would be the Chateau de l'Eperviere at Gigny-sur-Saone, between Chalon and Tournus. This actually has a fishing lake on site, as well as a good restaurant and take-away, indoor and outdoor pools and excellent showers etc. The Saone itself is a 10-15 minute walk away (or a 5 minute drive).
When you reach the river, you will see the 'Halte Nautique@ and there is plnty of space on the bank for fishing. There is in fact a simple camping area right by the river, with a sign that tells you to apply to the Mairie for permissuion to camp. It seems to be used as a long-stay area by French families - presumably anglers. Unless you are really into the simple life, I think l'Eperviere is to be preferred!
The e-mail address is domaine-de-leperviere@wanadoo.fr and the site appears in most of the standard guides (it is a Castels and Camping site).