This letter investigates the joint sensing problem between unmanned aerial vehicles (UAV) and base stations (BS) in integrated sensing and communication (ISAC) systems with fluid antennas (FA). In this system, the BS enhances its sensing performance through the UAV's perception system. We aim to maximize the communication rate between the BS and UAV while guaranteeing the joint system's sensing capability. By establishing a communication-sensing model with convex optimization properties, we decompose the problem and apply convex optimization to progressively solve key variables. An iterative algorithm employing an alternating optimization approach is subsequently developed to determine the optimal solution, significantly reducing the solution complexity. Simulation results validate the algorithm's effectiveness in balancing system performance.