Aurivillius oxides have been a research focus due to their ferroelectric properties, but by replacing oxide ions by fluoride, divalent magnetic cations can be introduced, giving Bi₂MO₂F₄(M = Fe, Co, and Ni). Our combined experimental and computational study on Bi₂CoO₂F₄ indicates a low-temperature polar structure of P2₁ab symmetry (analogous to ferroelectric Bi₂WO₆) and a ferrimagnetic ground state. These results highlight the potential of Aurivillius oxide-fluorides for multiferroic properties. Our research has also revealed some challenges associated with the reduced tendency for polar displacements in the more ionic fluoride-based systems.