For the 1996 24-hour race, Courage gave a C36 to the French racing team La Filière Elf and fielded two works cars itself. The Filière-C36, driven by Henri Pescarolo, Franck Lagorce, and Emmanuel Collard, finished seventh overall and second in the LMP-1 class after 24 hours. One of the two factory C36s, in which Mario Andretti was one of the drivers, finished 13th overall and third in the LMP-1 class.
In 1997, three C36s competed in Le Mans again, although Courage had once again built a new vehicle with the C41. Again the Filière car was the best-placed C36 with a seventh place.
In 1998 only one C36 was running on the Sarthe. Courage had severed its association with Porsche and equipped the new Courage C52 with a Nissan engine. At its last Le Mans appearance, the C36 finished 15th overall.