The spatial two-point coherence function of the thermal radiation field at subwave-distance from a metallic film is calculated within fluctuation electrodynamics. Long-range oscillations as a function of lateral separation are seen; we interpret their features by comparing to the dispersion relations of surface plasmon polariton modes on the thin film. The hybridization of the surface modes on the top and bottom interfaces leads to a beatnote in the field correlations, for specific detector setups.