Abstract: This paper investigates the sum-rate maximization problem in a multiple-input single-output downlink system integrating fluid antenna systems (FAS) and rate-splitting multiple access (RSMA). Since precoding design and fluid-antenna port selection are strongly coupled, the resulting optimization problem is a high-dimensional non-convex mixed-variable problem. To address this issue, a sum-rate maximization model is first established by jointly considering common-rate allocation, beamforming precoding, and port selection. Then, two solution methods are developed. The first is a low-complexity scheme based on port pre-selection, where the fluid-antenna port of each user is determined according to the maximum channel-gain norm criterion, followed by precoder optimization via successive convex approximation (SCA). The second is a Gumbel-Softmax-based joint optimization method, in which the discrete port-selection variables are continuously relaxed so that port selection and precoding can be optimized in an end-to-end manner. Simulation results show that the integration of FAS and RSMA achieves significant sum-rate gains over conventional antenna systems and conventional non-orthogonal multiple access schemes. The system performance improves with the number of ports, transmit power, and antenna aperture, while the gain gradually saturates due to spatial correlation. Moreover, under different signal-to-noise ratios, port numbers, and aperture settings, the proposed joint optimization method consistently outperforms the port pre-selection SCA scheme, demonstrating that joint design can better exploit the synergy between the spatial reconfigurability of FAS and the interference-management capability of RSMA.