Constant Djakpa was born on 17 October 1986 in Abidjan, Ivory Coast, starting to play football at Stella Club d'Adjamé.

[2][3] In the 2013–14 Europa League campaign, he appeared in four games for Eintracht in which he scored two goals in two victories from the group stage against Bordeaux and APOEL, both of them being from free kicks.

[16] Constant Djakpa played for the Ivory Coast Olympic team and for the country's under-21 side, representing the latter at the 2008 Toulon Tournament, scoring two goals, one from a penalty in a 1–0 win over United States and the other one in a loss in front of Chile.

[2][17] He played eight games for Ivory Coast's senior squad, making his debut on 21 November 2007 when coach Uli Stielike sent him on the field in order to replace Bakari Koné in a friendly which ended with a 6–1 away win over Qatar.

[19] Djakpa represented Ivory Coast at the 2014 World Cup, coach Sabri Lamouchi sending him on the field in 74th minute in order to replace Arthur Boka in a 2–1 victory against Japan from the group stage.