The purpose of this paper is to study two-person zero-sum stochastic differential games, in which one player is a major one and the other player is a group of N minor agents which are collectively playing, are statistically identical, and have the same cost functional. The game is studied in a weak formulation; this means in particular that we can study it as a game of the type "feedback control against feedback control." The payoff/cost functional is defined through a controlled backward stochastic differential equation, for which the driving coefficient is assumed to satisfy strict concavity-convexity with respect to the control parameters. This ensures the existence of saddle point feedback controls for the game with N minor agents. We study the limit behavior of these saddle point controls and of the associated Hamiltonian, and we characterize the limit of the saddle point controls as the unique saddle point control of the limit mean-field stochastic differential game.