After a 2-1 victory over a star-studded PSG side on Wednesday, Marseille are one of the favourites in a competition they have not won since 1989 and will host Annecy at Stade Velodrome.
Fellow Ligue 1 contenders Lyon also received a favourable draw following their win over Lille on penalties in the last 16 as they were paired with Ligue 2 club Grenoble.
Laurent Blanc's men have struggled in the league, where they currently sit ninth, and are banking on success in the French Cup to save their campaign when they host regional neighbours Grenoble.
Defending champions Nantes, who came through a tense penalty shootout to defeat Angers in the previous round, will entertain Lens in the quarter-finals.
Lens, who are third in Ligue 1 and level on points with second-placed Marseille, defeated Lorient on penalties on Thursday in the last 16.