In this letter, we investigate the security of fluid antenna system (FAS)-reconfigurable intelligent surfaces (RIS) communication systems. The base station (BS) employs a single fixed-position antenna, while both the legitimate receiver and the eavesdropper are equipped with fluid antennas. By utilizing the block-correlation model and the central limit theorem (CLT), we derive approximate expressions for the average secrecy capacity and secrecy outage probability (SOP). Our analysis, validated by simulation results, demonstrates the effectiveness of the block-correlation model in accurately assessing the security performance. Moreover, simulation results reveal that FAS-RIS system significantly outperforms other systems in terms of security, further underscoring its potential in secure communication applications.