A mesoscopic model for a polymer-based magnetoelectric (ME) composite film is developed. The film is assumed to consist of a piezoelectric polymer matrix of the PVDF type filled with CFO-like single-domain nanoparticles. The model is treated numerically and enables one to obtain in detail the intrinsic distributions of mechanical stress, polarization and electric potential and helps to understand the influence of the main configurational parameters, viz., the poling direction and the orientational order of the particle magnetic anisotropy axes on the electric response of the film. As the model is fairly simple-it uses the RVE-like (Representative Volume Element) approach with a single-particle cell-the results obtained are rather of qualitative than quantitative nature. However, the general conclusions seem to be independent of the particularities of the model. Namely, the presented results establish that the customary ME effect in composite films always comprises at least two contributions of different origins, viz., the magnetostrictive and the magnetoactive (magnetorotational) ones. The relative proportion between those contributions is quite movable depending on the striction coefficient of the particles and the stiffness of the polymer matrix. This points out the necessity to explicitly take into account the magnetoactive contribution when modeling the ME response of composite films and when interpreting the measurements on those objects.