Zinc oxide (ZnO) epitaxial thin films grown on c-sapphire substrates by pulsed laser deposition were investigated using angle and polarization-resolved photoluminescence spectroscopy. Side-emission spectra differed significantly from surface-emission spectra in exhibiting dominant, narrow, polarization-resolved peaks. These spectral features were attributed to leaky substrate modes in the layers. Observations were first verified using transmission calculations with non-adjustable parameters, which took into account the dispersion, the anisotropy of the ZnO refractive index and the dependence on film thickness. Results were consistent with Fabry-Perot-like interference being the origin of the distinctive ZnO luminescence observed at grazing incidence angles. A second analysis, based on the source terms method, was used in order to retrieve the bulk emission properties, including the wavelength-dependent quantum yield and the emission anisotropy. While ZnO thin films were considered here, this analysis method can be extended to any luminescent thin film of similar geometry, demonstrating the potential of leaky mode analysis for probing passive and active material properties.