We theoretically study the transport properties of a single graphene layer between two insulating materials, i.e., a ferromagnetic EuO thin film and a nonmagnetic SiC substrate. An exchange interaction between the charge carrier spins in graphene and the localized magnetic moments in the ferromagnetic insulator is assumed. This proximity effect and the large spin fluctuations at temperatures close to the ferromagnetic transition temperature TC lead to spin disorder scattering, which is calculated using a Green's function technique. Numerical results indicate that at temperatures close to TC the contribution of the spin disorder scattering to the total electron mobility is clearly observable even in the case of a weak exchange interaction and a low background mobility of the graphene layer. This enables the experimental determination of the exchange interaction parameter using the present model and a simple resistivity measurement.