Ajaccio and Brest played out a goalless draw at the Stade Francois Coty.
The clean sheet was Mexican goalkeeper Guillermo Ochoa's first of the season, and ensures the Corsican team move above Nancy into 16th place.
Ajaccio missed the best chance of the game after they were awarded a penalty following Benoit Lesoimier's handball in the area in the 80th minute.
However, Brazilian striker Eduardo saw his spot kick saved by Brest keeper Steeve Elana.
Brest's 14th draw of the season also sees them move up a place, and they now occupy 11th by virtue of Lorient's defeat at the hands of Lille.
Ajaccio take on Dijon at home next Saturday, while Brest host Marseille at the Stade Francis-Le Ble.
