The concept of fluid reconfigurable intelligent surface (FRIS) upgrades the conventional reconfigurable intelligent surface (RIS) paradigm by empowering its reflecting elements with positioning reconfigurability. This letter aims to investigate the use of FRIS to enhance physical-layer security in a system, in which a multi-antenna access point (AP) communicates with a legitimate user device in the presence of an eavesdropper. Unlike RIS with fixed-position elements, FRIS can dynamically select an optimal subset of elements from a larger array of candidate locations. We aim to maximize the secrecy rate by jointly optimizing the AP's transmit beamforming, the selection of FRIS activated elements, and their discrete phase shifts. The resulting problem is a challenging mixed-integer nonlinear program (MINLP), which is NP-hard. To address this, we propose an efficient algorithm based on an alternating optimization (AO) framework. Within this framework, the beamforming subproblem is optimally solved in closed form using the generalized eigenvalue method, while the combinatorial subproblem of joint element selection and discrete phase design is handled via the cross-entropy optimization (CEO) method. Simulation results show that the proposed FRIS design significantly outperforms the conventional RIS counterpart and other baselines, demonstrating the substantial security gains by element positioning as the new degree of freedom (DoF).