Optical two-dimensional Fourier transform spectroscopy is implemented near 800 nm with active stabilization. Excitation pulse delay is stabilized during data acquisition and stepped with interferometric accuracy. The reference used for heterodyne detecting the complete transient four-wave mixing signal is also phase-stabilized. The phase evolution of the four-wave mixing signal during the initial evolution period and the final detection period is then measured and correlated. Two-dimensional spectra with absorption and emission frequency axes are obtained by Fourier transforms with respect to the corresponding time variables. Measurement performed on a GaAs multiple quantum well sample shows light-hole and heavy-hole exciton transitions as the diagonal peaks and coupling between these two resonances as off-diagonal peaks.