The Frenchman has signed a season-long deal with Le Mans in his homeland subject to international clearance.
The club play in the third tier of French football.
Damour arrived at Hearts in 2019 from Cardiff City, signing a four-year-deal having impressed for the Bluebirds.
However, his impact at Tynecastle Park has been minimal, making just 21 appearances, all of which arrived in his first season.
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The 30-year-old was involved in pre-season and was on the bench in Premier Sports Cup ties but never played any competitive minutes.
“He’s got to be playing,” he said.
“Loic is a tenacious tackler. Put him in the right position and he can destroy anything. You have to keep warning him to think about things, and to be careful if a card comes out."