We did not visit the castle and the park, will do it next time. But in the evening we recommend to come to the other side of the river. Here N 47 19.361 E 1 03.816 there is free parking and then you need to walk a little along the river. You will see a very picturesque view of the castle with beautiful evening light, which visitors of the park cannot see.
And few images from the drone.
Getting there: parking for visiting the castle N 47 19.771 E 1 03.981. Parking on the other side of the river N 47 19.361 E 1 03.816. By train go to Chenonceaux station, it is located right next to the castle.