Hy Martyn S, yes is possible, but on the edge, I did it two years ago with my Roberts 40' and 1,95 draft
, take care to not pass the3,40 mts air clearence for the bridges , I think with the high level on the rivers now that also gonna be less air to pass under the briges.
Look for the FLUVIACARTE N 21 is for the Vois Navigables of France
and is excelent gave you all the options on canals with max draft and clearence under bridges.
From CALAIS use canal Calais, then Canal du Nord, Oise until Cergy then Seine until Moret sur Loing (Saint Mammes), there go to Canal du Loing, Canal de Briare, Lateral a la Loire, Canal duCentre and the Basse Saone, Rhone and you will finish at Port Louis du Rhone where we are now.
Take special atention to Lockers personal at the exit of canal du centre and the entrance at the river Saone because you have a few hundred meters with very low water but with speed you can pass if you folow their recomendation.
Enjoy the center of France
We love chanels and main reason to change our boat with a new with lifting keel
Good luck and enjoy the trip.