Ligue 1 Wrap: Valenciennes relegated, Saint-Etienne seal European place
Ariel Jacobs' men needed to win to keep their hopes of survival alive but fell to a 1-0 defeat, with Maor Melikson adding to their misery with a missed first-half penalty.
Julien Faubert struck the decisive blow for Bordeaux in the 74th minute to confirm Valenciennes will be playing in Ligue 2 next season.
They join Ajaccio in the second tier and the bottom club fell to a 22nd defeat of the season as Jeremie Aliadiere gave Lorient a 1-0 win
The final place is far from decided, though, after Sochaux's miracle run continued.
Herve Renard's side have been in the bottom three since the third round of fixtures but their 2-0 over 10-man Nice moved them to within a point of safety.
A Nemanja Pejcinovic own goal and Jordan Ayew's fifth of the season were enough to extend Sochaux's unbeaten run to six games, while Nice had Dario Cvitanich dismissed with 11 minutes remaining.
Evian remain in their sights after a third consecutive league defeat.
Prince Oniangue secured a 1-0 win for Reims but Pascal Dupraz's men could have earned a point had Cedric Mongongu not missed an 85th-minute penalty.
Saint-Etienne secured a place in the UEFA Europa League next season after a 2-0 win over Montpellier.
Romain Hamouma and Mevlut Erdinc were on target in the opening 15 minutes of the second half to secure the victory, while Montpellier still need a point to guarantee their top-flight status.
Christophe Galtier's men could still claim a Champions League place in the final weeks, and Marseille will hope to join them after their 4-2 win over Lyon.
Two goals from Andre-Pierre Gignac plus first-half strikes from Souleymane Diawara and Florian Thauvin secured Marseille's win, with Arnold Mvuemba and Bafetimbi Gomis netting for Lyon.
The result means Marseille are two points behind their opponents in the final Europa League place.
Meanwhile, in mid-table, Toulouse and Nantes shared the spoils in a 1-1 draw at the former's home ground, with Papy Djilobodji seeing red for the visitors after an elbow on Wissam Ben Yedder.