Manchester United midfielder Fellaini scored two first-half goals before Radja Nainggolan and Eden Hazard, from the penalty- spot, added to the tally after the break.
Les Bleus replied through Mathieu Valbuena's second-half penalty and late goals by Nabil Fekir and Dimitri Payet.
It was France's second loss since the 2014 World Cup, coming just over two months after a 3-1 home defeat by Brazil.
"They were very efficient, we under-performed defensively, we were better after the break," France coach Didier Deschamps told reporters.
"We can't be hyper confident ahead of the Euro 2016, but we can't be too worried."
Deschamps's side got off to a good start but failed to really threaten while Belgium scored with their first chance.
Fellaini picked up the ball in the area after a poor clearance by the French defence and fired home from close range to put the visitors ahead after 17 minutes.
The towering Fellaini netted his fifth goal in three games for the national side, heading the ball past Hugo Lloris from Toby Alderweireld's cross after being left unmarked three minutes from the break.
Nainggolan made it 3-0 five minutes into the second half with a 25-metre strike, with Fellaini responsible for the set-up play.
France, who will play only friendlies until Euro 2016 kicks off on June 10 next year because they qualified as hosts, pulled one back three minutes later when Valbuena converted a penalty after Olivier Giroud was brought down in the box.
Koscielny, however, made the same mistake when he pushed Axel Witsel in the back, allowing Hazard to make it 4-1 with a perfectly-taken spot-kick.
One minute from time, second-half substitute Fekir fired past Thibaut Courtois after playing a fine one-two with Paul-Georges Ntep.
Payet further reduced the arrears after collecting a backpass from Moussa Sissoko one minute into stoppage time.
(Reporting by Julien Pretot; Editing by Douglas Beattie)
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