The calculated distance (air line) between Fontaines-sur-Saône and Montpellier is approximately 161 miles respectively 259 kilometers.
By car or train, the actual journey to Montpellier is certainly longer, as only the direct route (as the crow flies) between Fontaines-sur-Saône and Montpellier has been calculated here.
Air line (approximately)
259 kilometers
140 nautical miles