Fe-doped III-V ferromagnetic semiconductors (FMSs) such as (In,Fe)As, (Ga,Fe)Sb, (In,Fe)Sb, and (Al,Fe)Sb are promising materials for spintronic device applications because of the availability of both n- and p-type materials and the high Curie temperatures. On the other hand, (Ga,Fe)As, which has the same zinc-blende crystal structure as the Fe-doped III-V FMSs, shows paramagnetism. The origin of the different magnetic properties in the Fe-doped III-V semiconductors remains to be elucidated. To address this issue, we use resonant photoemission spectroscopy (RPES) and x-ray magnetic circular dichroism (XMCD) to investigate the electronic and magnetic properties of the Fe ions in a paramagnetic (Ga$_{0.95}$,Fe$_{0.05}$)As thin film. The observed Fe 2$p$-3$d$ RPES spectra show that the Fe 3$d$ states are similar to those of ferromagnetic (Ga,Fe)Sb. The estimated Fermi level is located in the middle of the band gap in (Ga,Fe)As. The Fe $L_{2,3}$ XMCD spectra of (Ga$_{0.95}$,Fe$_{0.05}$)As show pre-edge structures, which are not observed in the Fe-doped FMSs, indicating that the minority-spin ($downarrow$) $e_downarrow$ states are vacant in (Ga$_{0.95}$,Fe$_{0.05}$)As. The XMCD results suggest that the carrier-induced ferromagnetic interaction in (Ga$_{0.95}$,Fe$_{0.05}$)As is short-ranged and weaker than that in the Fe-doped FMSs. The experimental findings suggest that the electron occupancy of the $e_downarrow$ states contributes to the appearance of ferromagnetism in the Fe-doped III-V semiconductors, for p-type as well as n-type compounds.