 Konaté played a major role in the next two seasons for Fontenay, attracting interest from higher division clubs.At the end of the 2004–05 season, Fontenay were demoted from the CFA, despite finishing 11th in their group and this signalled the end of Konaté's time with the club.In July 2005, Konaté signed his first professional contract with then Championnat National side Chamois Niortais.