Cycling in the Loire Valley is greatly encouraged. If you haven't brought your own, you can hire bikes in several of the main tourist towns and there is an extensive network of bike paths, many of them dedicated and separate to the roads. A lot of people bring a bike with them on the plane or on the back of the car. Cycling is safe here and it's flat, travelling along the bucolic river valleys. Where the cycle path and the road share space, there are regular signs to remind roadusers that voitures, vélos,partageons la route.
In the village of Cour-Cheverny, as in most places, they have installed
some robust and practical looking bike racks and we nearly always see
cyclists on the routes between the major chateaux.
The Loire à Vélo website should give you much of the information you need to plan a cycling holiday here.