Four distinct classes of multiferroics are usually being discussed in the literature, in which ferroelectricity is respectively driven by electronic lone pairs, geometry, charge ordering, and magnetism. Each class has its own shortcomings for technological applications. Here, through a combined experimental and theoretical investigation, we propose a mechanism to achieve multiferroicity in a single phase by engineering the anionic network and creating local geometric distortions in fluorinated, vacancy-ordered brownmillerite Ca₂Mn₂O_5–xF_y. The system exhibits both ferroelectricity and an antiferromagnetic order above room temperature, pointing toward a novel route to multiferroicity by anion mixing.