The electrical and optical properties of fluorine impurities in ZnSe have been studied. Bulk and delta-doped ZnSe:F layers were grown by molecular beam epitaxy. Electrical measurements reveal evidence that a majority of fluorine impurities act as shallow donors. In delta-doped samples, we find strong photoluminescence due to the radiative recombination of fluorine donor bound excitons. We measured a fluorescence lifetime of less than 250 ps and determined the inhomogeneous line width to be below 2 meV at liquid helium temperature.