Yes, I admit, I'm prejudiced, I live and ride here for over ten years now, but I do honestly believe that cycling is very good in France! And definitely in the centre of France, the Allier. Either on a race bike (that would be me), a mountain bike or a road bike, maybe with a battery even, there are loads of nice roads, more or not so 'hilly', beautiful views... and small restaurants during your ride!
Since a couple of years, we have the same groupe of Belgians, staying with us for a week, doing every day something between 60 to 120 km. Recently, their wives are aloud to come with them and now they're having a 'group inside the group', on bikes with batteries! They're great people, getting along in a great atmosphère. Check their photo diary to see how such a cycling week rolls :
And if you don't want to bring your own bike, you can also rent, also with a battery, at a new company close by with the perfect name A bike at the Countryside, Un vélo à la Campagne :