We have theoretically investigated the conduction electronic structure of an n-type narrow ZnSe/(Zn, Cd, Mn)Se quantum well subjected to in-plane magnetic fields within the framework of effective-mass approximation. Due to the giant Zeeman splitting, a large spin splitting energy between the local bound spin-up and spin-down electrons is reached under moderate magnetic field densities at low temperature. Since the effects of the in-plane magnetic fields on the energy dispersion and the effective mass of the two-dimensional (2D) electrons are negligible, a fully spin-polarized free 2D electron gas is obtained in the narrow quantum wells. The dependence of the spin polarization of the 2D electrons on temperature is also explored.