It will be the first ever meeting between Connacht and Bourgoin. The French side were the inaugural winners of the competition and have twice been runners-up, including last season.
The news of the fixture details comes as ERC, the tournament organisers, announced the dates, kick-off times and broadcast coverage for the ground-breaking matches in which three Heineken Cup pool runners-up will contest the Amlin Challenge Cup quarter-finals with the tournament's five pool winners.
The only match between two Amlin Challenge Cup teams - Connacht and Bourgoin - will launch the weekend's matches in Galway on Saturday, April 10.
And British & Irish Lions outside halves Jonny Wilkinson and Stephen Jones could go head-to-head in the south of France on the Saturday night when Toulon take on the Scarlets at Stade Felix-Mayol.
The all-England match between London Wasps and Gloucester will be the first up on Sunday before quarter-final number 4 at Kingston Park Stadium.
2009/10 AMLIN CHALLENGE CUP QUARTER-FINALS:
All kick-off times local time -
SATURDAY, APRIL 10
CONNACHT v Bourgoin, 1pm (Eurosport)
Toulon v Scarlets, 9pm (FR4)
SUNDAY, APRIL 11
London Wasps v Gloucester, 2pm (Sky Sports)
Newcastle Falcons v Cardiff Blues, 3pm