We have recently proposed the revised spherical cap harmonic analysis (R-SCHA) modeling technique. The new mathematical functions represent faithfully the spatial variations of potential fields in a restricted area. In this paper, we tackle the inverse problem and outline the efficiency of the new basis functions with respect to real magnetic data. Processing simultaneously repeat stations, observatory, aeromagnetic, and CHAMP satellite data provides our first vector lithospheric field model over France, which extends from surface to 500 km of altitude. The magnetic field is represented with a minimum horizontal spatial representation of 40 km at the mean Earth radius. The magnetic lithospheric map consistency is confirmed with a comparison to known geological features. The model variation with altitude also suggests that the major French magnetic anomaly, the Paris basin anomaly, is produced by a deep-rooted geological structure. These results demonstrate the superiority of regional modeling over global modeling for delineating small-scale details in the lithospheric field. In view of forthcoming satellite missions, like Swarm, the revised spherical cap harmonic analysis method will help to accurately represent the lithospheric field for more detailed geological interpretations.