Chambly will meet Les Herbiers in the last four of the Coupe de France, guaranteeing a third-tier side will contest this season's final.
The Championnat National teams were paired together in Thursday's draw, leaving holders Paris Saint-Germain to play the winner of the outstanding quarter-final clash between Caen and Lyon.
Les Herbiers extended their cup run by beating Ligue 2 Lens on penalties, while Chambly stunned top-flight side Strasbourg thanks to a goal from Lassana Doucoure.
Quevilly were the last team from outside France's top two divisions to reach the final of the competition - they lost to Lyon in 2012.
Unai Emery's PSG still remain on course to secure a domestic treble after easing to a 3-0 win over rivals Marseille, in the process securing a semi-final berth in the Coupe de France for a fourth successive season.