  We study the Hanle and spin polarization recovery effects on resident
electrons in a monolayer MoSe$_2$ on EuS. We demonstrate that localized
electrons provide the main contribution to the spin dynamics signal at low
temperatures below 15~K for small magnetic fields of only a few mT. The spin
relaxation of these electrons is determined by random effective magnetic fields
due to a contact spin interaction, namely the hyperfine interaction with the
nuclei in MoSe$_2$ or the exchange interaction with the magnetic ions of the
EuS film. From the magnetic field angular dependence of the spin polarization
we evaluate the anisotropy of the intervalley electron $g$-factor and the spin
relaxation time. The non-zero in-plane $g$-factor $|g_x|\approx 0.1$, the value
of which is comparable to its dispersion, is attributed to randomly localized
electrons in the MoSe$_2$ layer.
