I would like to take a riverboat cruise through France. What are the companies that travel the entire country?
None for the entire country since all the waterways don't link up unless you go out into the Med, Channel, or Atlantic. Are you interested in a self-drive or a crewed boat? It makes a difference on which company does it.
Viking River cruises does: the Saone and Rhone rivers from Chalon-sur-Saone to Avignon; (travel in either dirction 8 days; the Seine from Paris-Rouen and back to Paris 8 days; or you can combine both cruises into one with a land transfer from Paris to Chalon-sur-Saone
We did the Viking River Paris-Rouen-Paris cruise a couple of years ago when it was Paris-Le Havre. Quite nice if you want slow travel, but don't be like the passengers on our boat who wanted luxury ocean cruising on a riverboat. We docked with Uniworld boats at a couple of ports, so you could check their itineraries as well.