The Karush-Kuhn-Tucker (KKT) optimality conditions and saddle point optimality conditions in fuzzy programming problems have been studied in literature by various authors under different conditions. In this paper, by considering a partial order relation on the set of fuzzy numbers, and convexity with differentiability of fuzzy mappings, we have obtained the Fritz John (FJ) constraint qualification and KKT necessary conditions for a fuzzy optimization problem with fuzzy coefficients, for first time. Owing to the help of the KKT optimality conditions, we then discuss, the saddle point optimality conditions, associated with a fuzzy optimization problem under convexity and differentiability of fuzzy mappings.