Despite the 13-point final margin, it was always a close-run contest - with each side enjoying varying periods of dominance, but scores sitting level for long periods.
The Cedars started the better of the two, scoring first through Anthony Layoun. France were good enough to steady their ship though, striking back a few minutes later through Bastien Ader.
France levelled scores via a penalty goal just after the 20-minute mark, with the 6-all margin lasting right through to the halftime siren when Travis Robinson scored out wide for Lebanon, placing his side in front at the break.
Trailing 12-6 at the change of ends, France worked hard to ensure they were first on the scoresheet after the break, with Ader grabbing a double off a clever high kick which he was able to snap up from a knock-back to score.
Lebanon re-took the lead ten minutes later with a high ball of their own ensuring late inclusion Adam Douehi could get his name in the book. An 18-12 lead for the Cedars didn't last too long - Damien Cardace grabbed France's third and proceedings were level once more.
With less than 15 remaining both sides stepped it up as best they could, but the French seemed to run out of legs, first when Mitch Moses grabbed a 75th-minute field goal, then conceding twice more in the final five minutes with Moses himself scoring a wonderful individual try before Robinson claimed his second and wrapped the contest with a comfortable late flow of points.
The win means Lebanon are in the box seat to claim the third available Quarter Final berth from Pool A, with most expecting Australia and England to fill the other seeds. Next week Lebanon face England in Sydney on Saturday night while France are against the might of Australia back in Canberra on Friday night.