In this study, we applied electron energy-loss magnetic chiral dichroism (EMCD), an electron counterpart of X-ray magnetic circular dichroism (XMCD), to a network nanostructured FePt L10 ordered alloy film to examine the relative orientation of magnetic moments between neighboring Fe and Pt atoms using the Fe-M2,3, Pt-O2,3, and Pt-N6,7 semi-core excitation spectra with transmission electron microscopy and electron energy-loss spectroscopy. EMCD signals were successfully extracted from a large number of spectra using a dedicated data analysis procedure to obtain sufficient noise statistics. Results showed that the relative sign relation of the EMCD signals between the Fe and Pt absorption edges was consistent with that of the theoretical dielectric tensor while assuming that parallel magnetic moments exist between neighboring Fe and Pt. We believe the results of this study can be applied to alloys with different nanostructures to determine whether the spin configuration depends on the size and geometry of the nanostructures.