Former Clontarf scrum-half James Hart also made an impressive debut for Racing 92 following his move from Grenoble but it wasn’t enough to prevent an opening night defeat for Ronan O’Gara’s men.
Madigan’s only miss from six kicks was in the last action of the night from inside his own half when he needed to wind down the clock.
“It was good to see some of the kicks off the ground going well, the kicking out of hand wasn’t my finest day but I’m working hard on that in training and hoping that’s going to click for me soon once I get a flow of a few games.
“I’ll go back and review the footage of it, have a look at the footage of the Toulouse game against Montpellier and prepare for next week. So it’s good to be up and running and for me it’s about growing week on week,” said Madigan.
Carter kicked three from four and showed awesome pace to get back and prevent Bordeaux winger Nans Ducuing from scoring an intercept fin one of the few try chances of the night.
“He showed some turn of pace to catch our winger, he showed he still has that area of his game with everything else.
"He’s a class act and he shows his value over a season. They have real depth, a big squad and I have no doubt they will be competing in the barrage at the end of the season,” added the Irish international.
Bordeaux led 6-3 at the break and three more penalties from Madigan ensured a winning start to his career.
Buttin; Ducuing (Rey 41), Dubie (Rey 22-35), Lonca, Connor; Madigan, Lesgourgues (Serin 59); Taofifenua (Poirot 45), Chambord (Auzqui 53), Cobilas (Clerc 49); Jones, Marais (Cazeaux 67); Madaule, Braid (Chalmers 56), Goujon.
Dulin; Rokocoko, Chavancy, Vulivuli, Andreu (Laulala 56); Carter, Hart (Chauveau 56); Afatia (Brugnaut 49), Szarzewski (Lacombe 61), Tameifuna (Ducalcon 50); Carizza (Dubarry 76), van der Merwe (Williams 50); Lauret, Missoup, Claassen.