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Just before the break, Evian doubled their lead when Aldo Angoula managed to turn the ball home following a scramble in the area from a corner.
After half time, Roy Contout powered a header at goal from close range as he met Marange's cross from the right only to see his effort saved by Hansen.
Nicolas Benezet nearly added a third for the visitors but his shot from inside the box was well stopped by Pele.
However, Evian were not to be denied and they did get their third goal in the 72nd minute when Sougou and Wass combined again and the Dane tapped home from close range.
Abdoulrazak Boukari came close to getting a consolation goal for Sochaux but his effort from outside the box went just the wrong side of the post, as his side's relegation was confirmed at the final whistle.