The electrification of the aviation industry is a major challenge to realizing net-zero in the global energy sector. Fuel cell (FC) hybrid electric aircraft (FCHEV) demonstrate remarkable competitiveness in terms of cruise range and total economy. However, the process of simply hybridizing different power supplies together does not lead to an improvement in the aircraft economy, since a carefully designed power system topology and energy management scheme are also necessary to realize the full benefit of FCHEV. This paper provides a new approach towards the configuration of the optimal power system and proposes a novel energy management scheme for FCHEA. Firstly, four different topologies of aircraft power systems are designed to facilitate flexible power flow control and energy management. Then, an equivalent model of aircraft hydrogen consumption is formulated by analyzing the FC efficiency, FC aging, and BESS aging. Using the newly established model, the performance of aircraft can be quantitatively evaluated in detail to guide FCHEA design. The optimal aircraft energy management is realized by establishing a mathematical optimization model with the reduction of hydrogen consumption and aging costs as objectives. An experimental aircraft, NASA X-57 Maxwell, is used to provide a detailed performance evaluation of different power system topologies and validate the effectiveness of the energy management scheme. The new approach represents a guide for future power system design and energy management of electric aircraft.