In a large area around Château La Barge you will find wonderful opportunities for cycling. With cycling your reach is just a bit greater than with a walk. Hill on hill. It requires at least 7 gears on your bike, but you get something for that. You cycle through quiet villages, over hills with beautiful views or through the woods. The only chance of encountering a car is on a D road. The other routs are yours.
There are a few apps with different possibilities in the neighbourhood.