However, despite having defeated the French side 25-13 at Kingsholm in October, Director of Rugby Nigel Davies is taking nothing for granted and has named a strong side.
May returns for his first appearance since late September, while Trinder last played in Mont de Marsan - the week before that previous Bordeaux meeting.
Also returning to the starting line up are Tim Molenaar, Dan Robson, Darren Dawidiuk, Dario Chistolini and skipper Jim Hamilton.
Talking to the local media ahead of the team's departure, Davies expressed his hope that he'll see a real reaction following last Saturday's defeat against London Irish.
"Europe is a difficult arena, whether you're in the Amlin Challenge Cup or the Heineken Cup.
"I always stressed how important the middle two games against London Irish would be, and we came out on the right side of those two games.
"Now we have to hammer home our momentum in this tournament, and we have to go to Bordeaux and get a result. It's as simple as that.
"I think we've got a very good team, an exciting team. And we're expecting to perform."
Rob Cook; Charlie Sharples, Henry Trinder, Tim Molenaar, Jonny May; Freddie Burns, Dan Robson; Nick Wood, Darren Dawidiuk, Dario Chistolini; Jim Hamilton (capt), Will James; Sione Kalamafoni, Akapusi Qera, Ben Morgan
Huia Edmonds, Dan Murphy, Shaun Knight, Peter Buxton, Gareth Evans, Dave Lewis, Mike Tindall, Martyn Thomas