Bourgoin clinched a berth in the last eight over of the Amlin Challenge Cup with a tense 18-9 win over Leeds Carnegie at Headingley on Sunday.
Both sides knew going into the game that victory would secure a group win, and tries from Jean-Francois Coux and Albert Vulivuli and eight points from the boot of Benjamin Boyet helped the visits to the quarter-finals.
"We didn't perform to the level that we have been doing. We'd won four of our last five but we were a long way short today," said Leeds director of rugby Andy Key.
"Everything was stacked in our favour going into the game. We fully appreciated the fact that we were playing a very good side that had reached the final last year, but we felt that, on our own patch, we could get the win.
"We wanted to take the chance to progress but we weren't able to do that."
The result finalised the draw for the quarter-finals, with Connacht qualifying as top seeds after an unbeaten campaign.
Michael Bradley's side have been joined in the last eight by Wasps, Newcastle, Toulon and Bourgoin.
Those sides are joined by Cardiff Blues, Gloucester and Scarlets who qualify via this season's Heineken Cup to complete the quarter-final picture.
Bourgoin face a tough trip to play Connacht in Galway in the last eight while Toulon will be at home to Scarlets.
In the other two fixtures, Wasps will host Gloucester in an all-English affair and Cardiff Blues will travel to Newcastle to face the Falcons.
Connacht v Bourgoin
Toulon v Scarlets
London Wasps v Gloucester
Newcastle Falcons v Cardiff Blues
The games are scheduled for the weekend of April 9/10/11.
For Leeds Carnegie:
Pens: Thomas 3
Tries: Coux, Vulivuli
Leeds Carnegie: 15 Jon Goodridge, 14 Jonny Hepworth, 13 Luther Burrell, 12 Henry Paul, 11 Lee Blackett, 10 Ceiron Thomas, 9 Scott Mathie, 8 Rhys Oakley, 7 Calum Clark, 6 Kearnan Myall, 5 Marco Wentzel (c), 4 Erik Lund, 3 Juan Gomez, 2 Vili Ma'asi, 1 Mike MacDonald.
Replacements: 16 Rob Rawlinson, 17 Gareth Hardy, 18 Phil Swainston, 19 Jon Pendlebury, 20 Tom Denton, 21 Joe Bedford, 22 Jason Strange, 23 Scott Armstrong.
Bourgoin: 15 Anthony Forest, 14 Albert VuliVuli, 13 Matias Viazzo, 12 David Janin, 11 Rudi Coetzee, 10 Benjamin Boyet, 9 MickaŽl Forest, 8 Yann Labrit, 7 Sylvain Nicolas, 6 Julien Frier, 5 Coenraad Basson, 4 Wessel Jooste, 3 Karena Wihongi, 2 Tone Alefa Kopelani, 1 Arnaud Tchougong.
Replacements: 16 Jean-Philippe Genevois, 17 Vincent Pelo, 18 Olivier Milloud, 19 Timothy Cowley, 20 Bogdan Leonte, 21 John Senio, 22 Alberto Di Bernardo, 23 Camille Levast.
Referee: John Lacey (Ireland)
Assistant referees: Brain MacNeice (Ireland), Olly Hodges (Ireland)
Television match official: Peter Ferguson (Ireland)