A groin injury kept back rower Muldoon out of the recent Magners League games against Leinster and Edinburgh.
Centres Niva Ta'auso (knee) and Keith Matthews (hamstring) and number 8 George Naoupu (hamstring) have recovered from their respective knocks to return to the starting line-up.
Meanwhile, England-capped prop Robbie Morris has been added to the westerners' replacements bench, having shaken off a calf injury.
In all, Connacht coach Michael Bradley has made four changes to the team that overcame Edinburgh in the Magners League last Friday.
There are two changes in the backs, with Ta'auso and Matthews resuming their centre partnership. Brian Tuohy and Aidan Wynne are the players to make way as Troy Nathan shifts to the right wing.
Up front, there have been alterations to the second row and back row. The province's most-capped player, Michael Swift, will be partnered by Mike McCarthy in the second row, while Johnny O'Connor has Muldoon and Naoupu for company in the back row.
Bernie Upton and Mike McComish have dropped to the replacements bench which includes out-half Miah Nikora, the kicker of the match-winning penalty against Edinburgh.
Bradley has appealed to supporters throughout the province to come out in force at the Sportsground on Saturday as Connacht look to continue their 100% record in this season's Amlin Challenge Cup.
With opponents Bourgoin not taking up their full issue of tickets, supporters will be able to purchase a limited number of tickets at the gate on matchday.
CONNACHT (v Bourgoin): Gavin Duffy; Troy Nathan, Niva Ta'auso, Keith Matthews, Fionn Carr; Ian Keatley, Frank Murphy; Brett Wilkinson, Sean Cronin, Jamie Hagan, Michael Swift, Mike McCarthy, John Muldoon (capt), Johnny O'Connor, George Naoupu.
Replacements: Adrian Flavin, Ronan Loughney, Bernie Upton, Mike McComish, Conor O'Loughlin, Miah Nikora, Aidan Wynne, Robbie Morris.