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.
France finished on 21 points with Bosnia, on 20, heading for the play-offs where they hope to secure a place in a major tournament as an independent nation for the first time.
"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."
Bosnia played some nice, quick passing football throughout but France, below par in the first half, increased the pressure after the break and were eventually rewarded.
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.
Dzeko then burst into the box after being set up by a Zvjezdan Misimovic flick, but was denied by the ever cool Lloris.
In the 24th minute, Miralem Pjanic raced down the right and found the unmarked Dzeko on the left, but the Manchester City striker fired wide despite looking set for a deserved opener.
Bosnia, however, were rewarded five minutes from the interval as Dzejo unleashed an exquisite curling shot inside the far post fom the edge of the area.
Les Bleus stepped up a gear after the break but proved too clumsy to unsettle the Bosnia defence.
Nasri came close in the 72nd minute but his powerful free-kick was deflected onto the bar by substitute keeper Asmir Begovic.
Begovic, however, was powerless when Nasri wrongfooted him from the penalty spot after Spahic's careless foul.
France, who are unbeaten in their last 15 games, created a string of chances in the closing stages but failed to convert.
