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,L-z,P-parallel to,T) ensemble, where N is the particle number, L-z the wall separation, P-parallel to the pressure parallel to the walls, and T the temperature. Fixing T and P-parallel to such that the corresponding bulk system is ferroelectric, and considering confined films with various thicknesses proportional to L-z, we first demonstrate that the long-range orientational order persists down to L(z)approximate to6sigma. We then specialize to the case L-z=7sigma, for which we investigate in detail the spatial and orientational structure as functions of P-parallel to. 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.