Diakhaté has been at Nancy since his youth, and made his Ligue 2 debut on 20 October 2001, playing the first half of the 2–0 win over LB Châteauroux. He played 25 league matches the following season, and appeared regularly for the club, although his 2003–04 season was severely disrupted by injury. 2004–05 brought Diakhaté favourable recognition, winning a place in France Football's team of the season. However, on 18 July 2007 it was announced that he had signed a contract with Ukrainian club Dynamo Kyiv. Diakhaté made his debut for Dynamo on 1 August 2007 in a league fixture against FC Chornomorets Odessa. Pape quickly established himself in the first team and even captained the club on occasion. A month later on 1 September he broke a collar bone in a match against FC Kharkiv, but once recovered returned to the team. On 16 December 2009 he left the Ukrainian club Dynamo Kyiv, and returned to France signing a half-year loan contract with AS Saint-Étienne. The following season he was loaned to Lyon and was relatively used.
On 26 August 2011 he signed for Spanish club Granada CF, for a club record €4,500,000 on a four-year contract.
He earned in 2004 also a full international call-up from Senegal. After Nancy's promotion to Ligue 1 in 2005, Diakhaté was also part of the Senegalese team that finished fourth in the 2006 African Cup of Nations.