There are lakes in many areas France - and in some so many that you'll never be far from one wherever you are - and many of them have public beaches and even waterslides and that sort of thing. There's an area north east of Troyes - the Parc Naturel Regional de la Foret d'Orient - with large lakes then just a bit further north-east the Lac du Der Chantecoq, there's a lake (man-made I think) at Langres, lots of small lakes around the village of Echourgnac in the Dordogne region, the Lac d'Issarles in the Ardeche region, which is a volcanic lake and deep blue and very clear - but also extremely cold - too cold for me to enjoy swimming there. Then there are the Lakes of Pont de Salars, Pareloup, and Villefranche de Panat in the Aveyron, the lakes of Saint Peyre, Raviere and Laozas in the Haute Languedoc, the Lac de Salagou near Clermont L'Herault - and these are just the ones we've visited, that I can remember the names of. There are thousands more.
The Aveyron/Lozere area is fabulous for rivers - particularly the River Tarn, Jonte and Dourbie. The Tarn is a lovely river for swimming, (and for canoeing if your children are old enough) with lots of campsites alongside the river. We also love 'wild swimming' (in preference to swimming pools to be honest), but prefer rivers to lakes as the water is usually clearer. The Tarn Gorges area also has fabulous scenery, with deep gorges and spectacular cliffs, some lovely villages, and if you're interested in wildlife there are all sorts of birds of prey, including reintroduced vultures (with a viewing area set aside for you to watch them on the clifftops), and otters and beavers in the rivers which are lovely to watch in the evenings, especially from your pitch on one of the campsites!
You can probably tell the Tarn/Jonte/Dourbie area is my favourite - but it also remains remarkably unknown to too many British people, so unlike the Dordogne you don't feel that you're in little England sometimes. See these websites for more information: http://www.gorges-tarn.com/?lang=en, and http://www.ot-gorgesdutarn.com/
There are also lots of lovely lakes in the Auvergne region - but this is a very high altitude region, and does tend to get colder at night even in summer.