Cardiff will allow long-serving Kevin McNaughton to leave this summer along with Danny Gabbidon and Nicky Maynard.
Highly-rated Atletico Madrid midfielder Saul Niguez has signed a new five-year contract.
A statement on the club's official website confirmed that Fernandez made the announcement to his players and the club's directors on Thursday.
Youth team coach Patrick Gabriel will take charge of the team on a caretaker basis.
Nancy prop up Ligue 1 with 11 points, eight adrift of safety, and only one win all season, which came on the opening day against Brest.
Fernandez's last match in charge brought them their first win in any competition since then, a 5-1 success against fifth-tier Dreux in the Coupe de France on Saturday.