Joseph-Monrose began his career playing for his local club in Bondy, AS Bondy, before moving to CRAF Liévin. He arrived at RC Lens in 2002. On 20 July 2008 he signed his first professional contract with the Pas-de-Calais-based side, which would keep him there until 2013.[1] He was given the number 34 kit. He made his professional debut on 13 October 2008 in Lens' 1–0 win over En Avant Guingamp coming on as a substitute playing 20 minutes.[2] On 11 January 2010, RC Lens loaned him to LB Châteauroux until 30 June 2010.
On 23 June 2017, Gabala FK announced the signing of Joseph-Monrose on a two-year contract,[3] with Gabala confirmed his release at the end of his contract on 4 June 2019.[4]
On 16 June 2019, Neftçi PFK announced the signing of Joseph-Monrose on a two-year contract.[5] On 26 June 2021, Neftçi confirmed the departure of Joseph-Monrose after they decided not to renew his contract.[6]