We propose a new spectral imaging method for Fizeau interferometers, based on double Fourier interferometry. It is possible to acquire two-dimensional spatial and one-dimensional spectral information of the sky by applying Fourier-transform spectrometer algorithm and the Van Cittert-Zernike theorem. This imaging scheme is referred to as double Fourier interferometry. We noticed that a delay axis in Michelson interferometers is equal to the axis of a fringe pattern on an image plane in Fizeau interferometers. Therefore, this new approach can acquire three-dimensional information of the sky using a linear array detector placed on the image plane. We formulated the new method and validated it by performing laboratory experiments. We performed image reconstruction based on the new method, and derived the spatial and spectral distributions of the source. Thus, the method was experimentally verified. Using the new method, it is possible to perform image reconstruction in principle, with brief observations for each baseline, and a delay-line system is not required as in a conventional interferometer. In addition, because the field of view is limited by the telescope's optical system, it can be easily widened. Therefore, this new method of spectral imaging will be used for future astronomical observations with Fizeau interferometers.