After Epinal, Turenne turned southeast. Snow and bad roads slowed the advance, as the men tired and food ran short. The French main body marched through Remiremont, meeting no resistance from the troops of the Duke of Lorraine, and entered Belfort on December 27. The French had now come to the southern end of the Vosges. From there, Turenne moved northeast, reaching Mulhouse in southern Alsace on December 29. Taking an enemy detachment by surprise there, Turenne gained a quick victory at the Battle of Mulhouse. As the new year began, the French struck due north at the enemy headquarters near Colmar. At the Battle of Turckheim on January 5, 1675, Turenne decisively defeated Bournonville. The latter was forced to evacuate Alsace and cross back over the Rhine at Strasbourg.