This letter considers the physical layer security performance analysis of an unmanned aerial vehicle (UAV)-assisted FSO communication system based on a Fisher-Snedecor F distributed turbulence fading channel. We consider the combined effects of atmospheric turbulence, pointing errors, atmospheric attenuation, and angle-of-arrival fluctuations on the chan-nel. The communication between two legitimate peers in the presence of an external eavesdropper is studied from the perspective of communication theory security. Specifically, under two different eavesdropping modes where an eaves-dropper is located close to the legitimate transmitter or receiver, we derive the exact closed-form expressions of the se-crecy outage probability and strictly positive secrecy capacity respectively. These analytical results are validated through Monte Carlo simulations. Furthermore, we also analyze the impact of various link parameters for both the main channel and the eavesdropping channel on the system's performance.