The much lower magnetic ordering temperature of multiferroic fluorides strongly limits their practical applications [J. F. Scott and R. Blinc, J. Phys. 23, 113202 (2011)]. In this paper, (010) oriented BaCoF4 films have been prepared on (0001) Al2O3 substrates by pulsed laser deposition. The clear observation of amplitude and phase hysteresis loops by piezoresponse force microscopy confirms the ferroelectricity at room temperature. In contrast to the antiferromagnetism in bulk BaCoF4 with a much lower Neel temperature of 69.6K [Eibsch€utz et al., Phys. Rev. B 6, 2677 (1972)], clear magnetic hysteresis loops are observed in BaCoF4 films, indicating the weak room temperature ferromagnetism. The nearly unchanged saturated ferromagnetic magnetization of about 30 emu/cm3 between 5K and 300K suggests that the Curie temperature of BaCoF4 films is much higher than room temperature. Exchange bias is clearly observed, with a blocking temperature of 250 K. Magnetoelectric coupling is demonstrated by the observed magnetocapacitance effect at room temperature. [ABSTRACT FROM AUTHOR]