The Frenchman joined City from Hibs on a free transfer last year and was discussing terms on a second season at the Rioch Arena.
However, he has not been able to agree terms with the Sky Blues and is now free to leave the club when his contract expires on June 30th.
Beuzelin scored only one goal (against Blackpool) last season in 32 starts plus eight substitute appearances. He was cautioned on eight occasions.