A lot depends upon the route/canal you take. We spent a week on the Canal du Nivernais. As I recall
, some of the bridges were in the 3m range. As in 3.00m. There are some canals with tunnels... Another goes OVER a bridge. This guide: Revue Fluvial voies navigables centre-bourgogne Canal de Bourgogne
shows, as you said, 3.4m "tirant d'air" for the Canal de Bourgogne ==== execept for one place, where it's less. You obviously need to pick a route
before you go. Be aware that lack of water- or too much- will close some canals at times. With the screwy weather
everyone's been having, you need to keep an eye on that too.