The calculated distance (air line) between Luxeuil-les-Bains and Grenoble is approximately 185 miles respectively 298 kilometers.
By car or train, the actual journey to Grenoble is certainly longer, as only the direct route (as the crow flies) between Luxeuil-les-Bains and Grenoble has been calculated here.
Air line (approximately)
298 kilometers
161 nautical miles