The cooperative tilting distortions of n = 2 Ruddlesden–Popper oxides can be utilized to break the inversion symmetry of the host lattice and induce ferroelectric behavior. Unfortunately the desired a–a–c+/a–a–c+ structural deformation is only stabilized in phases with extremely small structural tolerance factors, limiting the chemical scope of this symmetry breaking approach. Here we describe the influence of topochemical fluorination on the structural distortions of n = 2 Ruddlesden–Popper oxides and demonstrate that the conversion of La3Ni2O7 to La3Ni2O5.5F3.5 breaks the inversion symmetry of the perovskite double layers which constitute the Ruddlesden–Popper framework, by driving a change from an a–a–c0/a–a–c0 distortion in the parent phase to an a–a–c+/a–a–-(c+) distortion in the oxide–fluoride. In this instance, the symmetry breaking distortions of adjacent acentric perovskite sheets are antialigned, and as a result the inversion symmetry of the host lattice is broken locally, but not globally, resulting in an antiferroelectric structure. The breaking of local inversion symmetry in layered perovskite phases, in the absence of second-order Jahn–Teller active “distortion centers”, is an important step toward the realization of ferroelectric and multiferroic behavior in phases of this structure type.