Pressure has been mounting on the 48-year-old in recent days, with the bottom-of-the-table Montbeliard side having collected just two points from their first seven games this season.
A section of the club's fans called for his head during Saturday's 2-0 home defeat to Lille, and the midweek hammering looks to have prompted Hely to hand in his notice.
Club president Laurent Pernet will let Hely know on Thursday morning whether it has been accepted.
"It's been 20 months since I began fighting, alongside the coaching staff, players and managers," Hely was quoted by L'Equipe as saying at his post-match press conference.
"I saved the club twice but tonight, in the interest of the club, I have submitted my resignation."