In order to ensure the seamless coverage in places without power grid, wirelessly powered enhanced radio remote heads (eRRHs) using energy harvesting have been proposed in fog radio access networks (F-RANs). In this paper, to achieve efficient scheduling of hybrid energy powered eRRHs, the energy efficiency of a downlink F-RAN with capacity-limited fronthaul links is investigated, where the eRRHs are powered by the power grid or harvest energy from radio frequency signals. To maximize the energy efficiency, the beamforming vector of the transmitter and the user-centric clustering scheme are jointly optimized under fronthaul capacity and transmission power constraints. We apply some approximate techniques and generalize the relationship between weighted-sum-rate and weighted minimum-mean-squared-error problems to obtain a tractable formulation for the optimization problem. Accordingly, an iteratively algorithm is proposed. Simulation results are provided to show the performance of the algorithm.