Les Bleus, on the receiving end of a shock 1-0 home defeat by Belarus on Friday, went in front with a magical goal from Karim Benzema in the 72nd minute.
The striker collected the ball with his back to goal, rolled it with the sole of his boot and turned swiftly to squeeze past two defenders before scoring with an angled, left-foot shot.
Winger Florent Malouda made it 2-0 after 78 minutes, giving much-needed hope to new coach Laurent Blanc who is trying to rebuild the team after their poor World Cup showing in June.
Blanc, who took over from Raymond Domenech after the World Cup and lost his first two matches in charge, breathed a sigh of relief after the game.
"We started (the Euros) really badly and told ourselves we needed to pick up at least one point here," Blanc told reporters.
"The way we played we deservedly took three points. I'm not saying this is fantastic because we have won just one game out of two but this could be the start of something new."
FLARE THROWN
Bosnia, who beat Luxembourg 3-0 on Friday, could face sanctions after a flare landed on the pitch nine minutes from time.
Captain Emir Spahic picked up a microphone to ask the fans to calm down and the game resumed after a short break.
Bosnia coach Safet Susic, fondly remembered in France for a spell at Paris Saint-Germain in his playing days, said the visitors deserved to win.
"I can only commend the French team for being better," he said. "They dominated throughout the whole match and had many chances."
The home side rarely threatened but came close to scoring on 65 minutes when a superb free-kick from midfielder Miralem Pjanic was well saved by goalkeeper Hugo Lloris.
France, toothless up front and shaky at the back against Belarus, showed huge improvement and may have found the marksman they so badly need in Benzema.
The 22-year-old, back in the team after being overlooked for the World Cup in South Africa, showed his class throughout and nearly made it 3-0 with a superb volley that went just wide in added time.
