Unbeaten in their last 27 games against domestic opponents, PSG are attempting to lift the trophy for a record-extending 16th time.
Stade Briochin, from Saint-Brieuc in northwestern France, are enjoying their best ever run in the competition, stunning Nice with two late goals in a 2-1 victory.
They had already dumped out top-flight opponents Le Havre in the last 64 before overcoming second-division Annecy on penalties in the following round.
Brest, who play PSG in the Champions League knockout phase play-offs this month, avoided another meeting with Luis Enrique's team after being paired with Ligue 2 outfit Dunkerque in Thursday's draw.
Fourth-tier Cannes host second-tier Guingamp in the final week of February, while Angers are at home to Reims, who scraped past fifth-division Bourgoin-Jallieu on penalties after a 0-0 draw.
Coupe de France quarter-finals:
Brest vs Dunkerque, Cannes vs Guingamp, Stade Briochin vs Paris Saint-Germain, Angers vs Reims