The in situ magneto-optical Kerr effect in both the polar and longitudinal geometry is studied for fcc Fe films on Cu/sub 3/Au(100) between 1.7 and 7.5 atomic layers thick. In films with Fe coverages less than 4 monolayers (ML) we observe a perpendicular magnetic anisotropy at temperatures below 300 K. At T=160 k the films exhibit a continuous spin reorientation transition from a perpendicular to an in-plane magnetization in a narrow thickness range between 3.5 and 4 ML. According to the thickness dependence of the Kerr signal the individual layers order ferromagnetically, in contrast to the findings in the Fe/Cu(100) system. Distinct changes in the magnetic properties as a function of coverage may be related to different states of the film structure and morphology.