A systematic study of 160 heavy and superheavy nuclei is performed in the Hartree-Fock-Bogoliubov (HFB) approach with the finite-range and density-dependent Gogny force with the D1S parameter set. We show calculations in several approximations: with axially symmetric and reflection-symmetric wave functions, with axially symmetric and non-reflection-symmetric wave functions, and finally with some representative triaxial wave functions. Relevant properties of the ground state and along the fission path are thoroughly analyzed. Fission barriers, Q α factors, and lifetimes with respect to fission and α decay as well as other observables are discussed. Larger configuration spaces and more general HFB wave functions as compared to previous studies provide a very good agreement with the experimental data.