Wasps are currently one point above Bayonne in the race for one quarter-final place from Pool Three. The teams drew 13-13 in France last weekend.
The Aviva Premiership club are boosted by fly-half Stephen Jones, prop Tim Payne, lock Tom Palmer and back-row forward Billy Vunipola all returning to the side.
Elliot Daly, meanwhile, starts at full-back because skipper Hugo Southwell is sidelined by a hamstring strain suffered in Bayonne.
Southwell's absence means Haskell will lead the side tomorrow and the 27-year-old is anticipating a tough test against a French outfit brimming with talent.
"They are a side with a lot of rugby rock stars in their team and they can turn it on and cause you a lot of problems on their day, so we've got to play pretty well to get this win," Haskell said.
"We want to progress in this competition, like every competition we are competing in, and we've put ourselves in a decent position. We need to just back it up this Thursday.
"I was lucky enough to be involved in a side that got to an Amlin Challenge Cup final with Stade Francais, and I know that progressing throughout a cup campaign can give you a lot of confidence."
The Bayonne line-up includes former New Zealand wing Joe Rokocoko, ex-French international star Cedric Heymans, current Wales scrum-half Mike Phillips and Australian lock Mark Chisholm.
With Pool Three games to come against Newport Gwent Dragons and Mogliano next month, Wasps know that victory tomorrow is essential in their quarter-final quest.
"I was delighted with the commitment shown by the team in France last weekend, and I am looking for more of the same tomorrow night," Wasps rugby director David Young said.
"It's a win-or-bust tie for Bayonne, who come to Adams Park knowing they have to get something from the game, but it's no different for us really.
"If we want to control our own destiny in this competition then we've got to win."
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