Currently, they lie third in the table on four points, with Biarritz a point ahead of them and unbeaten Harlequins leading the way on nine points.
The westerners head into the game on the back of a frustrating one-point league defeat to Edinburgh, allied to a growing injury list that is severely hampering their chances of putting results together.
Head coach Eric Elwood admitted: "Yes, we're very thin on the ground. This week is a big occasion for us. We're all excited about the Heineken Cup and everybody wants to play.
"After last year's campaign, we want to step up and improve on what we did last year. Even with the unfortunate injuries, we really fancy ourselves against teams like Biarritz.
"As I said last week, the young lads really stepped up to the plate against Edinburgh. And I have every faith that they will step up again this week if asked to do so."
The province's latest injury setback saw captain Gavin Duffy limp off with a hamstring injury midway through the first half of the 24-23 loss to Edinburgh.
Duffy, who was playing on the wing due to Robbie Henshaw's good form at full-back, will unfortunately be out of action for four to five weeks.
For the Biarritz tie, Connacht will be without some of their key men from last season's historic first Heineken Cup win over Harlequins - Duffy, John Muldoon, Michael Swift and George Naoupu are all confirmed injury absentees.
Back rowers Thomas Anderson and Eoghan Grace both returned to training on Monday and will be available for selection. It is also hoped that hooker Ethienne Reynecke will make a welcome return to training this week.
With Swift ruled out and McCarthy still doubtful, Andrew Browne looks set to make his Heineken Cup debut for his native province.
The 25-year-old lock/flanker, a younger brother of Leinster's Damian Browne, has already played 16 times for the westerners in the Amlin Challenge Cup. Most recently, he has enjoyed a run of three successive starts in Connacht's engine room.
Now the former Ireland Under-20 international is itching to play his part in a big European night at a packed-out Sportsground.
"It will be mad here on Friday. That's the one thing I am really looking forward to," he said, previewing the visit of the French giants.
"At the Toulouse game last year I was in the crowd and it was unbelievable. And watching the lads running on to the pitch was unbelievable.
"You want to be there on the pitch and hopefully that will be me there this weekend soaking up the atmosphere and getting the win."
The Clan Terrace is completely sold out for Friday's Pool 3 tie (kick-off 8pm), but there is still limited availability in some other areas throughout the ground.
Connacht v Biarritz Olympique tickets are available to buy online here or you can purchase them directly from the Connacht Branch.