Hi Ian - we've only ever 'overnighted' in the area between Clermont Ferrand and home - and overnight sites are not the sort of thing you're looking for. We've stayed in municipal sites in several locations, but nothing with a pool on site.
I've just had a look at the Camping Cheques website (we use Camping Cheques and it's a good reference source for sites of a reasonable quality)and there's one site near to Clermont Ferrand - Indigo Royat, which looks OK - but I've never stayed there (the Auvergne volcanoes are lovely though). Just north, nearer to Vichy, is Beau Rivage Bellerive (never stayed there, either, but it looks a nice site too).
I'm sure you'll get someone with a more personal recommendation, and hope you have a great holiday.