The hosts trailed to Edin Dzeko's strike five minutes before half-time and needed a 78th minute spot-kick to secure a draw at the Stade de France. Nasri was tripped by Emir Spahic just inside the box and the midfielder clinically scored from the spot.
France began the final qualifier a point ahead of the Bosnians and needing at least a draw to qualify automatically as group winners for next year's finals in Poland and Ukraine.
"We played poorly in the first half and that was partly because of the game Bosnia played," France coach Laurent Blanc, who took charge of the national team in August 2010, told a news conference.
"I told the players that if they wanted to go to the play-offs they'd just have to play like that. It was a nerve racking match."
Bosnia coach Safet Susic said his side "gave everything."
"I am sad for my players who gave everything. I am proud of them and I hope we'll have more luck in the play-offs," said Susic.
"We controlled the game during 60 minutes but then we suffered physically."
France keeper Hugo Lloris dived to his right to palm away Senad Lulic's attempt in the fifth minute but Loic Remy wasted a great chance for the hosts whe he raced clear on goal, but a poor touch allowed Keeper Kenan Hasagic to smother.
Begovic, however, was powerless when Nasri wrongfooted him from the penalty spot after Spahic's careless foul.
