Optical 2D Fourier transform spectroscopy (2DFTS) provides insight into the many-body interactions in direct gap semiconductors by separating the contributions to the coherent nonlinear optical response. We demonstrate these features of optical 2DFTS by studying the heavy-hole and light-hole excitonic resonances in a gallium arsenide quantum well at low temperature. Varying the polarization of the incident beams exploits selection rules to achieve further separation. Calculations using a full many-body theory agree well with experimental results and unambiguously demonstrate the dominance of many-body physics.