Born in Arles, France, Givet started his professional career at Monaco as a left-back before moving to centre-back. He made his debut in a 2–2 draw against Guingamp in December 2000. He played for Monaco between 2000 and 2007, making 178 league appearances and scoring eight goals. The highlights of his time at the club were winning the Coupe de la Ligue in 2003 and reaching the UEFA Champions League final in 2004, where he missed out on a winner's medal with a 3–0 defeat against José Mourinho's Porto. He played a pivotal role in their success, making 13 Champions League appearances during the campaign. He made a name for himself in the 2003–04 season where he blossomed in the Monaco defense alongside Patrice Evra, Julien Rodriguez and Sébastien Squillaci.