The draw was made on Thursday, with Yzeure rewarded for their victory over Ligue 2 outfit Valenciennes with a visit from the holders.
French champions Paris Saint-Germain, meanwhile, will host fellow Ligue 1 side Nantes after battling their way past Bordeaux on Wednesday.
The only other all top-flight affair will come at the Stade Louis II, where Monaco are set to entertain either last season's beaten finalists Rennes or Reims.
Saint-Etienne will face third-tier opposition in the form of either Red Star or Marseille Consolat, while Ligue 1 strugglers Metz welcome Brest to Stade Saint-Symphorien.
There is also guaranteed to be a fourth-tier club in the Coupe quarter-finals after Croix Iris were drawn at home to Concarneau.
Elsewhere, Auxerre will visit Le Poire-sur-Vie and Boulogne host Quevilly, who sprang a shock by beating Ligue 1 side Bastia in the last 32.
The ties are scheduled to take place on March 10.
