We implement Bragg-like spectroscopy in a paraxial fluid of light by imprinting analogues of short Bragg pulses on the photon fluid using wavefront shaping with a spatial light modulator. We report a measurement of the static structure factor, S(k), and we find a quantitative agreement with the prediction of the Feynman relation revealing indirectly the presence of pair-correlated particles in the fluid. Finally, we improve the resolution over previous methods and obtain the dispersion relation including a linear phononic regime for weakly interacting photons and low sound velocity.