I have spent quite a lot of time at Chenonceau lately, and while Susan is inside the château I usually sit near (or in) Célestine.
Célestine always attracts attention
I rather suspect that the actual mill was on the southern bank associated with the weir, as the map shows a stream that looks suspiciously like a mill race, and usually a weir is necessary to keep water levels high enough to make a mill usable all the year round.
I have tried to discover more about this mill, but the only references on the internet are about a pair of camping sites - either side of the river - which share its name.
It's a nice place for a wander though.