We went north-south some years ago with a draft of 1.5m. It was quite dodgy at times ploughing through silt and mud. I don't think it has improved since!
Going down the Rhone in early September there was a lot
of water! Currents at times were up to 6.5 knots - exciting for us but a real problem for the few boats trying to get upstream.
If you're still interested you should check the VNF website for info about closures. A lot of the canals close for maintenance
during the winter and that will seriously limit your options.