We report Monte Carlo simulation results for a strongly coupled dipolar soft-sphere (DSS) fluid confined to a nanoscopic slit pore with structureless, nonconducting walls. The central topic of our investigation are the conditions under which the pore fluid can spontaneously order into a globally polarized (i.e., ferroelectric) state. Polarized states are observed in bulk DSS fluids at sufficiently low temperatures and high densities/pressures. The confined system is simulated in the (N,Lz,P∥,T) ensemble, where N is the particle number, Lz the wall separation, P∥ the pressure parallel to the walls, and T the temperature. Fixing T and P∥ such that the corresponding bulk system is ferroelectric, and considering confined films with various thicknesses proportional to Lz, we first demonstrate that the long-range orientational order persists down to Lz≈6σ. We then specialize to the case Lz=7σ, for which we investigate in detail the spatial and orientational structure as functions of P∥. It turns out that the transition from the globally isotropic to the globally polarized phase occurs at significantly lower pressures/densities than in the bulk, indicating that spatial confinement can support the onset of ferroelectric order. We explain this phenomenon within the framework of a simple mean-field theory based on the assumption that confinement effectively restricts orientational fluctuations, as suggested by the Monte Carlo results.