Multiferroic materials have simultaneous magnetic and ferroelectric long-range orders and can be potentially useful for a wide range of applications. Conventional ferroelectricity in oxide perovskites favors nonmagnetic electronic configurations of transition metal ions, thus limiting the number of intrinsic multiferroic materials. On the other hand, this is not necessarily true for multiferroic fluorides. Using molecular beam epitaxy, we demonstrate for the first time that the multiferroic orthorhombic fluoride BaCoF4 can be synthesized in thin film form. Ferroelectric hysteresis measurements and piezoresponse force microscopy show that the films are indeed ferroelectric. From structural information, magnetic measurements, and first-principles calculations, a modified magnetic ground state is identified which can be represented as a combination of bulk collinear antiferromagnetism with two additional canted spin orders oriented along orthogonal axes of the BaCoF4 unit cell. The calculations indicate that an anisotropic epitaxial strain is responsible for this unusual magnetic ground state.