Exeter Chiefs, the top-ranked Aviva Premiership club in the 2014/15 European Rugby Challenge Cup, have been drawn in Pool 2 along with Bayonne, Connacht and La Rochelle.
The draw for the second-tier competition was made ahead of the draw for the new European Rugby Champions Cup at Neuchatel in Switzerland.
Former internationals Simon Shaw and Scott Quinnell carried out the draw at the Stade de la Maladiere and Exeter chief executive Tony Rowe is already looking forward to next season’s competition.
He said: "It's a terrific draw for us. Obviously we have played Connacht before, both here at Sandy Park and over in Galway, but we've never faced either of the two French clubs.
"As a club we always enjoy facing the challenges of Europe and this season will be no different for us.
“In the past few years we have enjoyed some memorable trips across Europe and I've no doubt that many of our supporters will already be busy planning potential trips across the water."
London Irish were drawn on Pool 1 alongside Cardiff Blues, Grenoble and a qualifier, while Pool 2 features Newcastle Falcons, Stade Francais, Newport-Gwent Dragons and a qualifier.
Falcons director of rugby Dean Richards said: "It's a great pool but not an easy one for us. Stade Francais are a quality side full of stars. There's a lot of experience there and up until the last six weeks of the season Stade were right in the mix for the French championship.
"Newport Gwent Dragons have recruited well under Lyn Jones and again, are a great side that we're looking forward to playing against.”
Newly-promoted London Welsh face Edinburgh, Lyon and Bordeaux-Begles in Pool 4 and Gloucester will take on French pair Brive and Oyonnax in Pool 5 as well as Italian outfit Zebre.
Full pool draw:
Pool 1: Cardiff Blues, London Irish, Grenoble, FIRA 1 qualifer
Pool 2: Exeter Chiefs, Bayonne, Connacht, La Rochelle
Pool 3: Stade-Francais, Newport-Gwent Dragons, Newcastle Falcons, FIRA 2 qualifier
Pool 4: Edinburgh, Bordeaux-Begles, London Welsh, Lyon
Pool 5: Gloucester, Brive, Zebre, US Oyonnax
Round 1: October 16/17/18/19 2014
Round 2: October 23/24/25/26 2014
Round 3: December 4/5/6/7 2014
Round 4: December 11/12/13/14 2014
Round 5: January 15/16/17/18 2015
Round 6: January 22/23/24/25 2015