Of Togolese origin, Gakpé began his career playing with his local club UMS Pontault-Combault, whom AS Monaco share a partnership with. During his time in Pontault-Combault, he regularly attended sessions at the Clairefontaine academy. After being recommended to the Ligue 1 side by Pontault-Combault and Clairefontaine officials, he agreed to join the principality-based side in 2001.
Despite not having a professional contract to his name, he joined the first-team squad following the winter break of the 2005–06 season making his professional debut in a 1–1 draw against RC Lens on 22 January 2006. Not only did he start the match, but he also scored his first professional goal, scoring it in just the 7th minute. He went on to play in 13 more matches and added another goal to his tally as well.
Serge then signed his first professional contract on 4 January 2007, inking a three-year deal with the club. He has since added another year to the contract, which ties him to Monaco until 2011. Over the next three seasons, his playing time dramatically increased making 76 appearances and scoring 11 goals. His performances have caught the attention of several prominent European clubs such as English sides Sheffield Wednesday, Chelsea and Tottenham Hotspur, and Spanish giants Barcelona. He signed for French Ligue 2 club FC Nantes on 28 January 2011. At the end of January 2012, it was announced that Gakpé had signed for Belgian club Standard Liège on a season long loan.