Herve Renard's men, who had secured survival on the last day in each of the last two seasons, went into the game needing a win to complete a dramatic escape for the third consecutive year.
However, Sochaux could not deliver the goods this time around as Evian sealed safety thanks to a Daniel Wass double and a strike from centre-back Aldo Angoula.
At the other end of the table Lille secured a place in next season's UEFA Champions League by coming from behind to beat Lorient 4-1.
Christophe Galtier's men will be joined in Europe's second-tier club competition by local rivals Lyon, who qualified for the competition by marking coach Remi Garde's final game in charge with a 1-0 triumph at Nice.
That game was also marred by an injury to Steve Mandanda, part of France's squad for the FIFA World Cup, who suffered a jarring blow to the head in a challenge and left the field on a stretcher.
Elsewhere, Wissam Ben Yedder scored a hat-trick in Toulouse's 3-1 victory over Valenciennes, Rennes won 3-1 at Reims and Bastia and Nantes played out a 0-0 draw.
