Transport tips from Amboise to Chateau de Chenonceau

Take the train it is a short distance if you are not driving.
https://en.oui.sncf/en/
Or you can probably rent a bike

I had a rented bike (not just for the day). It's 22 km, each way. Some of it is on local roads, no major traffic. Most of it is on paved bike trail. From Amboise follow the bike trail along the south side of the Loire going toward Tours. As you reach the outskirts of Amboise (only a few blocks from the bridge) there is a sign to turn left, after that it's signed pretty well all the way to Chenonceau. The first mile or so is a fairly steep climb from the river, after that it's mostly easy rolling hills. There is a long slight downhill through a forest, which becomes a long gradual uphill on the way back, but nothing like the climb up from the river.

I wasn't aware of a train option?

We had rented a car. It is very easy to drive in Loire. The drive to Chenonceau from Amboise was easy and short.