Toulouse-Narbonne on a road bike?

Hi!
I've read through some older posts and comments here regarding routes in the south of France, and Bordeaux-Toulouse and Toulouse-Narbonne in particular. I do understand that touring trips and touring bikes are not the same as road bikes, so I'm trying to gather some info on the accesability of these routes to a road bike.

It was noted that the Bordeaux-Toulouse part is significantly better than the one to Narbonne as the path by along Canal du midi is rougher and quite bad at times. However does anyone have some experience to share in riding the Departement (D-roads) that often go along close to the canal? The general census on cyclists riding on the shoulder?

I do live in Toulouse, and along the part of the canal which passes my house there is usually a paved road raised a bit above the canal and a more dirt/gravel path closest to the water. This changes a bit going south with maybe one side being more accessible than the other etc. Is this representative for the canal broadly speaking? To Narbonne?

I've also looked alot at established routes (from Routeyou.com as an example). It seems like i'ts implied that there is a lot of dirt/gravel and uneasy terrain. Do you have any experience following such routes as a road cyclist? Is it easy to find alternative paved parts close to the canal?

While I do ride a road bike, I do have Continental Competition Pro Ltd RBX 28mm tires, which to my understanding (just bought a used bike) are more puncture resistant and made for cobbled terrain.

General input, experiences or alternative routes from Toulouse-Narbonne is also greatly appreciated, thank you!