The Saone river is wide and generally placid and has few locks. 

Burgundy is easily reached from Paris and a night in Dijon before and or after the trip is a must.

Burgundy is rich in history and famous world wide for her fine wines produced in the Beaune region. 

One week out and back cruises :

Saint Jean de Losne - Pont d'Ouche and back. From Saint Jean de Losne  take the Burgundy canal North through Dijon to Pont d'Ouche and back. This is a green and rural cruise through Dijon and on to the beautiful valley of the Ouche river. Hard work on the locks but good cyling all along the canal towpath.
140 km, 110 locks, 45 hr round trip cruising time

Saint Jean de Losne - Chagny and back. From Saint Jean de Losne take the river South to Châlon sur Saône then up the Canal du Centre to Chagny. Another good introductory trip with no difficulties and and a good range of scenery.
175 km, 28 locks, 35 hr round trip cruising time
H2O recommended first time trip

Saint Jean de Losne - Louhans and back.
293 km, 16 locks, 38 hr round trip cruising time

Saint Jean de Losne - Besançon and back.
150 km, 48 locks, 32 hr round trip cruising time

Fontenoy le Château - Gray and back.
200 km, 30 locks, 35 hr round trip cruising time

Fontenoy le Château - Charmes and back.
130 km, 130 locks, 43 hr round trip cruising time

Saint Jean de Losne - Fontenoy le Château or vice versa. This is a quiet introduction to canal and river cruising. The river section is wide and tranquil and the canal section further north is more compact. A small amount of locks makes this a good cruise for those with less experience and less energy to spend on winding lock gate handles.
160 km, 33 locks, 32 hr one way trip cruising time
H2O recommended first time trip

One week, one way cruise :

Saint Jean de Losne - Branges or vice versa. This is a quiet introduction to river cruising with very few locks. The cruise is on the Saône and the Seille. Highlights : Seurre, Chalon sur Saône, Tournus.
143 km, 6 locks, 19 hr one way trip cruising time