The global transition to a clean and sustainable energy infrastructure does not stop at aviation. The European Commission defined a set of environmental goals for the “Flight Path 2050”: 75% CO2 reduction, 90% NOx reduction, and 65% perceived noise reduction. Hydrogen as an energy carrier fulfills these needs, while it would also offer a tenable and flexible solution for intermittent, large-scale energy storage for renewable energy networks. If hydrogen is used as an energy carrier, there is no better device than a fuel cell to convert its stored chemical energy. In order to design fuel cell systems for passenger aircraft, it is necessary to specify the requirements that the system has to fulfill. In this paper, a statistical approach to analyze these requirements is presented, which accounts for variations in the flight mission profile. Starting from a subset of flight data within the desired class (e.g., mid-range inter-European flights) a stochastic model of the random mission profile is inferred. This model allows for subsequent predictions under uncertainty as part of the aircraft design process. By using Monte Carlo-based sampling of flight mission profiles, the range of necessary component sizes, as well as optimal degrees of hybridization with a battery, is explored, and design options are evaluated. Furthermore, Monte Carlo-based sensitivity analysis of performance parameters explores the potential of future technological developments. Results suggest that the improvement of the specific power of the fuel cell is the deciding factor for lowering the energy system mass. The specific energy of the battery has a low influence but acts in conjunction with the specific power of the fuel cell.