This paper presents a unique hybrid type aircraft propulsion system which combines a commercial turbofan system with a solid oxide fuel cell system. Thermodynamic analyses and parametric studies are collectively performed to investigate the compatibility and applicability of the proposed system as well as its performance through the energetic and exergetic efficiencies to determine how the efficiencies are affected by varying the operating conditions. Hydrogen, methane, methanol, ethanol, and dimethyl ether with different combinations are chosen as alternative fuels to replace kerosene, which is a traditional, fossil-based fuel. It is found that the net power of the solid oxide fuel cell is 944 kW with an electric efficiency of 87.0%. A maximum thermal efficiency of 32.3% and exergetic efficiency of 43.9% were achieved using 75% methane and 25% hydrogen fuel. The maximum overall thermal and exergetic efficiencies of the hybrid turbofan are 48.1% and 54.4%, respectively, using 75% methanol and 25% hydrogen fuel, which reduce carbon emissions by 65% compared to the fossil fuels. Therefore, the hybrid turbofan aircraft engine can increase the turbofan performance. In addition, a fuel mixture of 60% ethanol and 40% hydrogen can increase the performance by 5% and reduce carbon emissions by 73%.