Australia, playing in their second final, were left to rue a poor kicking performance as they failed to convert first-half tries by Mark Nawaqanita and hooker Lachlan Lonergan.
They also missed two penalties in the second half in a game that had seven lead changes, with French hooker Theo Lauchaud and prop Alex Burin both crossing in the first half.
France held an 18-13 advantage at the break but Australia's Harry Wilson scored his side's third try to put the Junior Wallabies up 20-18.
Carbonel, who had been instrumental in France's campaign last year, then slotted two of four penalties, his final successful kick giving the French the 24-23 advantage.
"The scoreboard shows how close the match was," said Australia captain Fraser McReight.
"It was back-and-forth and just point after point from each team. Credit to France, they played really well but I am super gutted for my team.
"We really lifted the tempo in the second half but unfortunately that wasn't enough to get the job done."
South Africa beat hosts Argentina 41-16 to clinch third place while England finished fifth after a 45-26 win over Wales.
Six-times champions New Zealand beat Ireland 40-17 but their seventh-place finish was their lowest since the tournament began in 2008.
(Reporting by Greg Stutchbury in Wellington; Editing by Peter Rutherford)
