In only their second season in the Amlin Challenge Cup, the Chiefs have reached the last eight by beating Perpignan and the Newport Gwent Dragons twice. Now comes the ultimate test for one of the new forces in English rugby.
"This is the biggest game the club has ever played - we've never been at this level before," said Hayes, who has led his side to six wins in their last seven outings.
"There was a lot of euphoria attached to our promotion wins against Bristol, and to certain wins in the Premiership, but when you look at it the Amlin Challenge Cup is probably the highest level of competition the club has ever played in.
"This is the rugby we all want to be playing in and there's no point in us being afraid of being here. We have to try and enjoy the challenge.
"We realise they've got some massive names and Stade has been a marquee name in rugby for 10 or 15 years now. But they're the big challenge that we have to relish and we have to face up to."