I don't see any connections from Bayeux to Dijon, for instance, that don't go through Paris. In Paris, you must connect stations by taxi or other public transport. The leg from Bayeux is an unreserved regional train an arrives at Gare St. Lazare. Then, you can choose to travel from Paris Gare de Lyon to Dijon by reserved TGV (1.5 hours) or from Paris Bercy station to Dijon by cheaper regional train (3 hours).
How to Look Up Train Schedules and Routes Online gives you the DB train schedule link and tips for using it. To find the slower trains to Dijon, try a search with "means of transport = without ICE."