While time-resolved infrared (IR) vibrational spectroscopy provides insight on structural dynamics of solution-phase systems, current techniques are limited to high concentrations. Fluorescence-encoded infrared spectroscopy (FEIR) can be used to encode IR-driven vibrational excitations into excited electronic states that fluoresce, which can be detected at lower concentrations than a coherently detected IR signal. Here, we report on the development of Fourier transform FEIR as an alternate approach for high-sensitivity IR spectroscopy. Upon driving vibrational excitation with a pair of IR fields with a variable time delay, an interferometric component was observed in the encoded fluorescence. This signal can be Fourier transformed to obtain a vibrational spectrum. By additionally varying the time delay of the encoding pulse following the second IR pulse, we observed frequency-difference oscillations, allowing us to construct a 2D correlation spectrum of coupled vibrations. Response functions for this experiment have been modeled, which reproduce the observed spectral features and relate them to excitation pathways using diagrammatic perturbation theory. The pathways observed in a 2D FEIR spectrum arise from the excitation of vibrational populations and coherences between coupled vibrations.