The appearance of sixth-generation networks has resulted in the proposal of several solutions to tackle signal loss. One of these solutions is the utilization of reconfigurable intelligent surfaces (RIS), which can reflect or refract signals as required. This integration offers significant potential to improve the coverage area from the sender to the receiver. In this paper, we present a comprehensive framework for analyzing the secrecy performance of a RIS-aided mixed radio frequency (RF)-free space optics (FSO) system, for the first time. Our study assumes that a secure message is transmitted from a RF transmitter to a FSO receiver through an intermediate relay. The RF link experiences Rician fading while the FSO link experiences Málaga distributed turbulence with pointing errors. We examine three scenarios: 1) RF-link eavesdropping, 2) FSO-link eavesdropping, and 3) a simultaneous eavesdropping attack on both RF and FSO links. We evaluate the secrecy performance using analytical expressions to compute secrecy metrics such as the average secrecy capacity, secrecy outage probability, strictly positive secrecy capacity, effective secrecy throughput, and intercept probability. Our results are confirmed via Monte-Carlo simulations and demonstrate that fading parameters, atmospheric turbulence conditions, pointing errors, and detection techniques play a crucial role in enhancing secrecy performance.