The five-time champions won a thrilling semi-final to progress into the decider against the United States in Madrid on Sunday.
The Serbs were on top for the majority of the contest in the Spanish capital, but endured a 39-point final quarter from the French to keep their noses in front and advance.
Nicolas Batum did his best to get the French over the line, shooting 35 points - which included draining eight threes from 12 attempts.
However, Milos Teodosic led the Serbs' scoring with 24 points - including five threes from seven attempts - and had five team-mates in double-figures in scoring.
Bogdan Bogdanovic (13), Nenad Krstic, Miroslav Raduljica, Steven Markovic (all 11) and Nemanja Bjelica (10) also contributed.
France only held the lead for 21 first-quarter seconds, and trailed by as much as 18 points late in the first half.
And despite only cutting the deficit to 15 with a quarter to play, Vincent Collet's men produced an almighty surge to give the Serbs a scare.
Batum netted 17 last-quarter points in a stirring cameo, but ultimately, France fell short of reaching a maiden gold-medal match.
France can win their first medal at the event, in the bronze medal match against Lithuania on Saturday.