The Romanian side Timisoara complete the section, with the first round of European fixtures to take place on the weekend of 13/14/15/16 October followed by round two a week later.
The match against English Premiership side Harlequins could see a reunion with Edinburgh’s record try scorer Tim Visser, who now plays for the London club. Scotland internationalist and former Glasgow player Ruaridh Jackson is also now at Harlequins after moving from Wasps this summer.
When Edinburgh reached the final of this event in 2014-15 it was played at Twickenham Stoop, the home of Harlequins, and Alan Solomons’ side lost 19-13 to Gloucester.
Fallen Paris giants Stade Francais are two-time runners-up in the Champions Cup but are in the Challenge event this year after finishing a disappointing third-bottom in the Top 14 last season.
Romanian league winners Timisoara Saracens are a partner club of European champions Saracens.
The finals of next season’s European Champions Cup and European Challenge Cup will be played at BT Murrayfield in May.
EUROPEAN CHALLENGE CUP DRAW 2016-17
Pool 1: La Rochelle, Gloucester, Treviso, Bayonne
Pool 2: Ospreys, Grenoble, Newcastle, Lyon
Pool 3: Brive, Worcester, Dragons, Enisei-STM
Pool 4: Cardiff, Bath, Pau, Bristol
Pool 5: Harlequins, EDINBURGH, Stade Francais, Timisoara Saracens