Agossi, whose mother is from France and whose father is from Benin, began her career as the protege of Archie Shepp. In her youth, she lived with her mother, a Mathematics professor, in Niger, Morocco and the Ivory Coast. She began her career as a theater actress; in 1993 she sang in a Swing- and New Orleans Jazz Band, with whom she toured in France and Ireland. She finally shifted her to Modern Jazz and henceforth sang under her own name. Since then, she has worked in a trio composed of vocals, bass and drums and linked her Jazz with different musical elements, such as Chanson and Rock Music. Aside from their own compositions, they also covered Monk's "Well You Needn't", Jimi Hendrix's "Voodoo Child", Pink Floyd's "Money" and The Beatles's "And I Love Her". After years in Spain she returned to France and then moved to Great Britain in 1993, where she worked with Vincent Guérin.

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After the album Voice & Bass, she became increasingly famous in the French Jazz Scene and also appeared in the United States. Her album EZ Pass to Brooklyn was recorded with Alexander Hiele (Bass) und Bertrand Perrin (Drums) in New York in 2001, which was influenced by the September 11 attacks. This album was a stylistic blend of Hip-Hop and R&B. Since her album Well You Needn't (2005), she performed for Candid and was accompanied by Ichiro Onoe (Drums) and Eric Jacot (Bass). She performed at the Festival International de Jazz de Montréal in 2007 and in Blue Note in New York. In 2010 she worked on (Just Like a Lady) with guitarist and composer Phil Reptil.

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Agossi was nominated for the ADAMI in 2005 and for the Victoires du Jazz in 2006. In December 2010 she was knighted as a Chevalier dans l'ordre national du Mérite.