We describe and implement an interferometric approach to decay-associated photoluminescence spectroscopy, which we term decay-associated Fourier spectroscopy (DAFS). In DAFS, the emitted photon stream from a substrate passes through a variable path length Mach-Zehnder interferometer prior to detection and timing. The interferometer encodes spectral information in the intensity measured at each detector enabling simultaneous spectral and temporal resolution. We detail several advantages of DAFS, including wavelength-range insensitivity, drift-noise cancellation, and optical mode retention. DAFS allows us to direct the photon stream into an optical fiber, enabling the implementation of superconducting nanowire single photon detectors for energy-resolved spectroscopy in the shortwave infrared spectral window (lambda = 1-2 mu m). We demonstrate the broad applicability of DAFS, in both the visible and shortwave infrared, using two Forster resonance energy transfer pairs: a pair operating with conventional visible wavelengths and a pair showing concurrent acquisition in the visible and the shortwave infrared regime.