Fluid antenna system (FAS) is emerging as a key technology for enhancing spatial flexibility and sensing accuracy in future wireless systems. This paper investigates an unmanned aerial vehicle (UAV)-enabled FAS for multi-target wireless sensing in low-altitude wireless consumer networks (LAWCNs) for achieving the low-altitude economy (LAE) missions. We formulate an optimization problem aimed at minimizing the average Cramér-Rao bound (CRB) for multiple target estimations. To tackle this non-convex problem, an efficient alternating optimization (AO) algorithm is proposed, which jointly optimizes the UAV trajectory, the antenna position of the transmit fluid antennas (FAs) and the receive FAs, and the transmit beamforming at the UAV. Simulation results demonstrate significant performance improvements in estimation accuracy and sensing reliability compared to conventional schemes, e.g., the fixed position antenna scheme. The proposed system achieves enhanced sensing performance through adaptive trajectory design and beamforming, alongside effective interference suppression via the flexible FAS antenna repositioning, underscoring its practical potential for precision sensing in the UAV-enabled LAWCNs.