Fontenay is probably the best preserved Cistercian abbey I have visited. As is customary for Cistercian abbeys, it's located along a river valley and you will recognize the usual structures with refractory, chapel and fish ponds. What is missing, are any interior decorations. The abbey was closed during the French revolution and turned into a paper factory for a century thereafter. At the beginning of the 20th century, a rich French banker bought the estate and began the restoration of the site. The family to this day owns the property.
The most similar site I have visited is Maulbronn. The main difference is that Maulbronn is more lively as it has more interiors and decorations left and a small town grew around it.
Getting There
Fontenay is near the town of Montbard. Montbard proudly advertizes the fact that they are a TGV stop. Which is kind of true as the TGV between Djion and Paris stops there a few times a day. Alternatively, there also (slower) regional trains that connect you to both Dijon and Paris. Note: The TGV requires a reservation and is frequently fully booked; I ended up having to take the regional train back to Paris. The train schedules in general (as is the case for most of France) are infrequent and cumbersome.
From the train station, I had to walk as there was no bus connection. It's roughly 6km. Problem is that the best footpath is not on google maps or signposted, so I had to walk along a busy road for a while. On my way back, I followed the dedicated trail and came out a bit outside Montbard at D980. The last bit of the walk, when you follow the river into the valley, is really nice
While You Are There
Repeating myself re French public transport: It's terrible. Looking at the map, you would think that you could easily combine a visit to Fontenay with a visit to Vezelay (45km apart). But you can't. Vezelay does not even have a bus connection or anything. Meanwhile, if you are by car, this is easily feasible. Seeing you will need to take a cab to Vezelay anyhow, it may be worthwhile to simply catch on in Montbard.