We introduce a new method, called entangled photon-pair two-dimensional fluorescence spectroscopy (EPP-2DFS), to sensitively probe the nonlinear electronic response of molecular systems. The method incorporates a separated two-photon ('Franson') interferometer, which generates time-frequency-entangled photon pairs, into the framework of a fluorescence-detected 2D optical spectroscopic experiment. The entangled photons are temporally shaped and phase-modulated in the interferometer, and are used to excite a two-photon-absorbing (TPA) sample, whose excited-state population is selectively detected by simultaneously monitoring the sample fluorescence and the exciting fields. In comparison to 'classical' 2DFS techniques, major advantages of this scheme are the suppression of uncorrelated background signals, the enhancement of simultaneous time-and-frequency resolution, the suppression of diagonal 2D spectral features, and the enhancement and narrowing of off-diagonal spectral cross-peaks that contain information about electronic couplings. These effects are a consequence of the pure-state field properties unique to a parametric down-conversion light source, which must be included in the quantum mechanical description of the composite field-molecule system. We numerically simulate the EPP-2DFS observable for the case of an electronically coupled molecular dimer. The EPP-2DFS spectrum is greatly simplified in comparison to its classical 2D counterpart. Our results indicate that EPP-2DFS can provide previously unattainable resolution to extract model Hamiltonian parameters from electronically coupled molecular dimers.