Wasps, the 2004 Heineken Cup winners, will entertain Brian O'Driscoll's Leinster for the first time in tournament history, while Munster face a difficult away tie against Welsh challengers Llanelli Scarlets.
Northampton, who qualified as one of two best runners-up from six pools, face a reunion with top seeds Biarritz, probably in San Sebastian.
The Saints lost 17-8 at home to Biarritz on Sunday, and will travel as rank outsiders against a side contesting their fifth successive quarter-final.
Heineken Cup quarter-final line up:
Biarritz v Northampton, Llanelli Scarlets v Munster, Wasps v Leinster, Leicester v Stade Francais.
Ties to be played on weekend of March 30-April 1.