The interaction of germanene, the germanium counterpart of graphene, with (0001)ZnSe surfaces is investigated theoretically, using first-principles simulations. On a non-reconstructed (0001) ZnSe surface, germanene is predicted to be metallic, due to the pinning of the Fermi level by Se surface states. On a reconstructed (0001)ZnSe surface, which should be more energetically stable for very thin layers, the germanene layer is found to be semiconducting, with an energy band gap of about 0.4 eV. Remarkably, the nature (indirect or direct) and magnitude of this energy band gap can be controlled by an out-of-plane electric field, a semiconductor to metal transition being predicted for electric fields larger than about 0.6 V/Å.