Chris,
Generally barges are rather expensive, multi-day (usually a week) experiences with, as you saw in that episode, sleeping facilities and dining provided.
However, Les Canalous provide half-day or one (or more) day boat rentals if you wish to pilot a boat yourself. These are "sans permis," which means you don't need to possess any kind of specialized license to rent them. They offer half-day or daily rentals from their facilities in three cities, one of them (Digoin) in Bourgogne.
If you want to just ride a boat on a canal with someone else doing the piloting, there are fewer opportunities that I'm aware of (unless you want to approach someone with a boat tied up at a "halte nautique" and offer them a few hundred euros to sail around with your for a couple of hours).
One option is, again, in Digoin. I believe it's run by Les Canalous, but it's marketed as Croisière-Digoin. Located about 90 minutes by car southwest of Beaune, they offer trips for an hour or so or ones with catered lunch or dinner periodically. See here for their schedule and contact information.
Digoin is an old industrial city that lies near several canals, including the generally east-west Canal du centre, which was the original division during WWII between occupied France to the north and Vichy France to the south, the Canal de Roanne à Digoin, which heads south to Roanne, and the Canal latéral à la Loire. One interesting aspect of that canal is it crosses over the Loire River on the Pont-Canal du Digoin (bridge canal), built in the early 1800s. It was built to allow commercial boat and barge traffic to carry goods over the Loire River.
When we first moved to Bourgogne, we didn't know the post-canal even existed. My wife and I were having a picnic lunch along the Loire and we could see what we assumed was just a normal bridge maybe 1,000 feet away. As I munched on my baguette sandwich, I saw what looked like a boat crossing the bridge over the Loire. I assumed it was on a trailer being hauled by a truck, but when it got to the same side of the river we were on, I saw no truck or trailer. We decided to walk over to see what it was, and that's when we learned about this somewhat unusual feature. There are several in France and probably elsewhere, but it was the first time I'd seen one.
