Single-crystal films of (001)Zn1-xFexSe (x=0.017, 0.027, 0.043) grown by molecular beam epitaxy on (001)GaAs have been studied using reflectivity and photoluminescence spectroscopies. Data have been obtained over the temperature range 4-77 K in magnetic fields up to 8 T in the spectral region near the band gap of 2.8 eV. The luminescence spectra show the two lowest interband excitonic transitions. From these spectra, the Zeeman splitting of the bands and the corresponding Fe2+-band electron exchange integrals were determined. The temperature dependence of the band splitting was determined through reflectivity measurements. These studies confirm the fact that Zn1-xFexSe exhibits Van Vleck paramagnetism and yield the spin-orbit splitting of the lowest Fe2+ crystal field states.