Entropy stable discontinuous Galerkin methods for nonlinear conservation laws replicate an entropy inequality at semi-discrete level. The construction of such methods depends on summation-by-parts (SBP) operators and flux differencing using entropy conservative finite volume fluxes. In this work, we propose a discontinuous Galerkin-Fourier method for systems of nonlinear conservation laws, which is suitable for simulating flows with spanwise homogeneous geometries. The resulting method is semi-discretely entropy conservative or entropy stable. Computational efficiency is achieved by GPU acceleration using a two-kernel splitting. Numerical experiments in 3D confirm the stability and accuracy of the proposed method.