The Irish province then face back-to-back games against Worcester Warriors in December, before the return fixtures against Montpellier and Madrid in January.
The dates and times of Connacht's final two group games have yet to be confirmed.
Connacht's 2009/10 European Challenge Cup Pool 2 fixtures:
Friday, October 9: Connacht v Olympus Rugby XV Madrid, The Sportsground, 7pm
Friday, October 16: Montpellier v Connacht, Stade Yves du Manoir, 8pm
Saturday, December 12: Worcester Warriors v Connacht, Sixways Stadium, 3pm
Friday, December 18: Connacht v Worcester Warriors, The Sportsground, 7pm
January 14-17: Connacht v Montpellier, The Sportsground, kick-off tbc
January 21-24: Olympux Rugby XV Madrid v Connacht, Estadio Universidad Complutense, kick-off tbc