Flexible antenna arrays (FAAs) can physically reshape their geometry to add new spatial degrees of freedom, whereas transmit beamforming adjusts the complex element weights to electronically steer and shape the array's radiation pattern, thereby significantly improving communication performance. This paper is the first to explore the integration of FAA geometry control and beamforming for physical layer security enhancement, where a base station equipped with an FAA communicates with a legitimate user in the presence of passive eavesdroppers. To safeguard confidential transmissions, we formulate a new secrecy rate maximization problem that jointly optimizes the transmit beamforming vector and a continuous FAA shape control parameter. Due to the non convex nature of the problem, an alternating optimization algorithm is developed to decompose the joint design into tractable subproblems, which are solved iteratively to refine both the FAA geometry and beamforming strategy. Simulation results confirm that the proposed joint optimization framework significantly outperforms conventional fixed shape or beamforming only schemes, demonstrating the potential of FAA enabled reconfigurability for secure wireless communications.