The rocksalt-type ferromagnetic (FM) insulator EuS (bulkT_C = 17 K) grown on Bi₂Se₃with well-matched (111) plane of the film and (0001) plane of the substrate is studied. The system may feature magnetic proximity effect breaking the time-reversal symmetry and opening a bandgap in the metallic topologically protected surface state of Bi₂Se₃. The experimental X-ray diffraction studies are combined with ab initio calculations to resolve contradictory results concerning the enhancement of the T_C up to 300 K and the degree of induced magnetization in the system. It is concluded that previous studies relied on idealized and unconfirmed structure models. Herein, it is shown by surface X-ray diffraction (SXRD) with ab initio calculations that a two double layer-thick EuS film grows with a sharp interface and without chemical intermixing in a single domain state in an FCC-type stacking on the Bi2Se3(0001) surface in which the topmost layer is metallic, thereby lifting polarity. A large p_z-orbital-derived top-layer sulfur magnetic moment of 0.6 μ_B is found, whereas for europium, μ_Eu = 6.9 μ_B throughout the film is found. No magnetization within the first Bi₂Se₃quintuple layer is found. The calculation of the exchange parameters J_ij indicates a complex FM and antiferromagnetic ordering between europium and sulfur with a maximum Neel temperature of 226 K.