We demonstrate a Fourier spectrometer that uses intense ultrashort laser pulses. By exciting the 6S(1/2) - 8S(1/2) two-photon transition in atomic cesium vapor, we are able to measure the small hyperfine splitting of the 8S(1/2) excited state. This technique, combining a high spectral resolution with the high peak intensities available to femtosecond laser systems, may offer intriguing opportunities for the study of multiphoton transitions and for spectroscopy in the short-wavelength region.