Chances were few and far between in a largely uneventful first half at Stade Auguste-Delaune II.
The visitors created the first meaningful chance of the encounter in the 22nd minute when Benoit Tremoulinas took a shot from outside the box, but failed to keep it on target.
Then six minutes before the half-time interval, Henri Saivet also tried his luck from distance but in vain.
Both sides continued to create chances as the second half progressed, with Gregory Sertic shooting wide in the 67th minute.
Two minutes later Ayite was unlucky not to score for Reims when his shot from the left side of the Bordeaux box came off the crossbar.
In the 73rd minute Reims had another chance to break the deadlock as Bocundji Ca shot just wide, and minutes later Sertic was denied by Kossi.