The Corsican club finished 16th in their first season in the top flight, two places and three points above relegation.
Club president Alain Orsoni had hoped to retain the services of the 45-year-old, but accepts his decision to move on.
Orsoni said in a statement on the club's official website: "Olivier has decided not to continue in his post.
"The decision is his and must be respected. We had a long discussion and, despite my disappointment, I have no choice but to accept his decision.
"He leaves with my gratitude and affection. He was the architect of our promotion and managed to consolidate us last season under difficult conditions.
"On behalf of the entire club, officials, staff and players, I express our appreciation of a talented coach and a man of conviction.
"Whatever his reasons for stepping back, we are confident he will bounce back in his career and that very soon he will be back on the football field.
"We wish him good luck for the future."