The home side made the brighter start when Mathieu Dossevi brought a good save out of Jesper Hansen with a curling effort in the third minute.
Evian responded with a chance of their own just five minutes later, but Cedric Cambon's header at the far post flew wide across the face of goal from a Cedric Barbosa cross.
The teams continued to trouble one another in an end-to-end first half, but neither could break the deadlock heading into the break.
Dossevi had another opportunity to put Valenciennes ahead on the hour mark, but his run ended with him dragging his shot across the face of goal.
However, the game finally had it's first goal just seven minutes from time when Sougou made the most of some poor defending from Valenciennes to turn and fire into the back of the net from inside the box.
Valenciennes stay bottom of Ligue 1, while Evian move up to 15th.