This letter studies the impact of fluid antenna system (FAS) technology on the performance of unmanned aerial vehicle (UAV)-assisted multiuser communication networks. Specifically, we consider a scenario where a fixed-position antenna (FPA) base station (BS) serves K FAS-equipped users with the assistance of a UAV acting as an aerial relay. The BS employs rate-splitting multiple access (RSMA), while the UAV operates in half-duplex (HD) mode using the decode-and-forward (DF) strategy. For this system, we derive a compact analytical expression for the outage probability (OP) and its asymptotic behavior in the high signal-to-noise ratio (SNR) regime, leveraging the multivariate t-distribution. Our results show how deploying FAS at ground users (GUs) in UAV-aided communications improves overall system performance compared to using FPA GUs.