The magnetic properties, morphology, and crystallographic structure are studied for Fe films on Cu₃Au(100) grown at room and low temperature, using in situ magneto-optical Kerr effect, scanning tunneling microscopy, and electron diffraction techniques. At T=160 K a spin-reorientation transition from perpendicular to in-plane magnetization occurs in films with Fe coverages starting from a critical thickness of 3.5 and 5.5 ML for room-temperature and low-temperature growth, respectively. Close to the critical thickness we observe an fcc-bcc structural transformation. The spin-reorientation transition is shown to be correlated to this structural change. This correlation may be explained by a drastic reduction of the perpendicular anisotropy induced by the fcc-bcc structural transformation.