We introduce an effective-medium theory for the local field and mean dielectric function of a polymer dispersed liquid crystal (PDLC) film consisting of identical spherical liquid crystal droplets dispersed in a polymer matrix. The theory takes account of the tensor nature of the dielectric response of the liquid crystals and the subsequent re-orientation of the liquid crystal tensor inside the PDLC droplets, as well as the presence of other droplets. We present explicit numerical results for droplets with radial and bipolar director boundary conditions as a function of external voltage.