Troyes must win their final game of the campaign and hope that Sochaux lose theirs to have a chance of avoiding immediate relegation to Ligue 2.
It took nine minutes for the first opportunity of the game to come when Camus came close to giving Troyes the lead, but his shot went over the crossbar.
The hosts came close six minutes later, but Jean-Christophe Bahebeck's long-range drive flew just past the far post.
Troyes had another chance midway through the first half when Stephane Darbion's cross following a corner was met by Bahebeck, but his header glanced just wide.
It took Troyes 11 minutes into the second half to take the lead when Bahebeck slid through Camus, who slotted his effort in the bottom corner of the net.
Bordeaux's chances of recovering were dealt a blow with 25 minutes left to play when Julien Faubert was sent off.
Obraniak came close to finding a leveller three minutes later, but his effort from outside the box just went wide.
Bahebeck was fractions away from an equaliser with 14 minutes to go, but he shot just wide from the edge of the six-yard box following Nivet's cross.