The frequency locking of a cold atom fountain clock is achieved by synchronizing the center frequency of an externally injected microwave signal with the atomic transition frequency, thereby obtaining a highly accurate frequency reference. In conventional systems, the detected frequency error signal is processed by a digital PID controller to generate a correction term that adjusts the microwave center frequency accordingly. To facilitate optimization of the fountain clock locking process, a simulation model of the frequency locking loop is developed using Python. Two key parameters of the model are determined from experimental data. The standard deviation of the additional Gaussian white frequency noise during locking is σ/τ=1.35×10-13（for τ=2.4 s）, and the proportional coefficient between the measured transition probability difference and the frequency error is C=2.8. Based on this model, a fuzzy PID control scheme is introduced into the frequency locking loop to enable dynamic tuning of the PID parameters, thereby enhancing system robustness and disturbance rejection capability. The simulation framework is first employed to optimize and select relevant experimental parameters, followed by short-term experimental measurements under both conventional PID and fuzzy PID control conditions. Both simulation and experimental results show that the fuzzy PID controller provides superior short-term frequency stability compared to the traditional PID method. Allan variance analysis indicates an improvement of approximately 14.2% in short-term stability, and the strong agreement between simulation and experimental results confirms the validity of the developed simulation model. Furthermore, independent simulations show that the fuzzy PID controller exhibits effective suppression of sudden frequency jumps (±1×10-11) while maintaining a comparable response speed to the conventional PID under systematic frequency steps (±5×10-12).