Chagny has much better train connections with Beaune. There are trains roughly every 30 minutes. Cost is €3.70 for the one-way ride. There are no ticket agents so you have to use the machine. Unfortunately, the machine takes only coins or a chip-and-pin credit card. Since we had neither, we relied on the kindness of an elderly couple who purchased our tickets with their credit card and then we paid them with euros.
Train station in Chagny.
Be sure to use the underground passage instead of crossing the tracks to get to the platform for Beaune trains.