France showed a marked improvement after losing 78-4 to Samoa and 82-0 to England, but Lebanon claimed a 24-20 golden-point victory in both teams' final World Cup match.
Lebanon led 20-18 when captain Alex Twal and France prop Julian Bousquet were sin-binned after a clash in the 77th minute.
France fullback Arthur Mourgue then kicked a two-point field goal to level the scores, after Lebanon halfback Alex Conti's goal-line drop-out went astray.
France five-eighth Cesar Rouge appeared to win it with a golden-point field goal, but video review penalised France for obstruction before fulltime.
After a penalty against centre Guillermo Aispuro-Bichet, Conti's long-range attempt missed. Mourgue chipped the ball, but Abbas Miski caught it and scored Lebanon's winner.
Conti scored Lebanon's opening try, kicked four goals and set up tries for Tony Francis and Michael Gabrael. France scorers included Amir Bourouh and Aispuro-Bichet, while Rouge's 71st-minute try kept his side close.
The win gave Lebanon coach Michael Cheika a high note before his return to the NSW Waratahs.