A previous study of the growth conditions has shown that single-phase BiFeO₃ thin films can only be obtained in a narrow pressure-temperature window and that these films display a weak magnetic moment. Here, we study in more detail the structure and the magnetism of single-phase BiFeO₃ films by means of reciprocal space mapping, Raman spectroscopy and neutron diffraction. X-ray and Raman data suggest that the BiFeO₃ structure is tetragonal for 70 nm thick films and changes to monoclinic for 240 nm thick films, thus remaining different from that of the bulk (rhombohedral) structure. In the 240 nm monoclinically distorted film, neutron diffraction experiments allow the observation of a G-type antiferromagnetic order as in bulk single crystals. However, the satellite peaks associated with the long-wavelength cycloid present in bulk BiFeO₃ are not observed. The relevance of these findings for the exploitation of the magnetoelectric properties of BiFeO₃ is discussed.