Wife and i cycled part of the route Teetosugars is proposing last year, the section from Orleans to Chinon, apart from one or two sections where the sign posted cycle route took you up the valley sides, cycling was relatively flat and easy going. quiet roads/cycle tracks and don’t recall any chicane type barriers you get on the cycle paths here so trailer is no problem.
We rode a tandem and borrowed a trailer from my LBS, first time i used it was getting on the ferry at portsmouth. takes a bit of getting used to, but fit all camping kit clothes etc for me an the wife. the only time we noticed it was going uphill, where the bike felt draggy and trying to get around in town. Tight turns or trying to reverse the bike ended in jack-knifed frustration.
I did find a rack bag useful in addition though (for shopping, easy access tools, puncture kit etc) roll top bag was a faff if you needed anything on the move.