Arthur Mourgue's mistake in golden point turned France's late push into a 24-20 win for Lebanon at CommBank Stadium on Sunday.
The match was a dead rubber, but both sides played with pride in one of the tournament's most compelling contests.
Mourgue had forced extra time with a two-point field goal from 40 metres in the 80th minute.
France then looked to have won with a field goal from Cesar Rouge, but Thomas Lacans was penalised for obstruction and the score returned to 20-20.
Mourgue attempted a chip-and-chase, sending the ball into Abbas Miski's hands; Miski raced over for the winning try in the 85th minute.
Earlier, Alex Conti opened the scoring after starting and finishing Lebanon's first attacking move, four minutes into the match.
France responded through Amir Bourouh's penalty try after the bunker ruled Moustafa Dirani had dislodged the ball with his foot during the grounding attempt.
Despite making ten first-half errors, Lebanon held an 8-6 lead at the break.
Michael Gabrael extended the Cedars' advantage, but Guillermo Aispuro-Bichet, Tony Francis and Rouge scored as the sides traded tries.
Rouge's 71st-minute try tied the game at 18-18, before Conti's penalty goal put Lebanon ahead 20-18.
France threatened again in the final seconds, but Lebanon were ruled to have grounded a fumbled ball in-goal.
Julian Bousquet and Lebanon captain Alex Twal were sin-binned late in the match.
Conti earned player-of-the-match honours, recording a try, two try assists, three tackle breaks, two penalty goals and 114 run metres.