the link below states there are numerous trails just to the South of Caen-
http://sitesvtt.ffc.fr/trace-vtt/suisse-normande-6/
but the website it links to doesn’t have a map, which is unusual.
It seems most of the towns in France encourage their local bike groups to use and “manage” the trails, and the tourist offices produce a map giving info’ on the trails.
We spent some time around Verdun (wrong side for you) and whilst the trails weren’t particularly challenging, there was some fun to be had, and most of them went through the woods and trenches of the battlefields. I wasn’t prepared for the scale of it all, completely amazing and quite humbling at times.