Here's a first suggestion for a route from Caen to the Chateau, already including mmmmartin's very helpful advice on the approach to the chateau.
http://www.gpsies.com/map.do?fileId=gddpgrrdbefgniar
It't 76 miles according to GPSies (in reality I would expect it to be closer to 80). I'm quite confident about the route apart from the part on the N13 between Saint Come du Mont and Valognes (approx. mile 51 to mile 67). It seems to be the straightest way, and apparently the N13 ceases to be a dual carriageway north of Saint Come du Mont, but traffic might be an issue. Alternatives would add some milage.
Any ideas by anyone?