He announced his decision to the Montferrand players and management after his side were beaten 30-22 to Bristol in Round 5 of the Heineken Cup.
It was their second successive home defeat in the Heineken Cup this season.
The France international flanker said:"I made this decision after due reflection and it has not been made solely as a result of the defeat to Bristol.
"I feel the players need to take their responsibilities seriously and I hope that my decision will help the tam in the long run.
"I must face up to my lack of success in passing on the coaches' message on the field.
"I continue to believe in this team which has real qualities but everyone must ask themselves some serious questions in order to move forward."
Montferrand, quarter-finalists of last season, have had a disappointing Heineken Cup campaign, winning just once so far - an opening day victory against 47-12 Swansea - but since then all results have gone against them, leading to Magne's resignation.
Montferrand face Swansea in their final pool match on Saturday.