In this study, the implementation of a solid oxide fuel cell–gas turbine hybrid engine for primary propulsion and electric power generation in aircraft is investigated. The following three parameters, which are crucial in attaining optimal performance at any point in the flight profile, were identified: the oxygen-to-carbon ratio of the catalytic partial oxidation reformer, the fuel utilization factor of the fuel cell, and the airflow split ratio at the outlet of the high-pressure compressor. The study assesses the impact of varying these parameters within specified ranges on the performance of the hybrid system. At the design point, the system yielded a total power output of 1.96 MW, with 102.5 kW of electric power coming from the fuel cell and 7.9 kN (1.86 MW) of thrust power coming from the gas turbine. The results indicate that varying the oxygen-to-carbon ratio affected the fuel cell’s fuel utilization and resulted in a slight decrease in gas turbine thrust. The fuel utilization factor primarily affected the power output of the fuel cell stack, with a minor impact on thrust. Notably, varying the airflow split ratio showed the most significant influence on the overall system performance. This analysis provides insights into the system’s sensitivities and contributes to the development of more sustainable aircraft energy systems.