Federated learning (FL) over wireless networks is fundamentally constrained by unreliable communication links, particularly when uplink channels suffer from blockage, fading, or weak line-of-sight (LoS) conditions. Pinching-antenna systems (PASSs) offer a new physical-layer capability to dynamically reposition radiating points along a dielectric waveguide, enabling controllable LoS connectivity and significantly improved channel quality. This paper develops FedPASS, a novel framework for low-latency wireless FL assisted by PASS. We formulate a multi-objective optimization problem that jointly minimizes the end-to-end round latency and an upper bound on the FL optimality gap. The resulting formulation is a mixed-integer nonlinear program subject to practical constraints on scheduling, transmit power, local CPU frequency, and PA placement. To address the resulting computational challenges, we develop a two-tier iterative algorithm: an outer loop that updates scheduling, communication time allocation, and power control via block coordinate descent, and an inner loop that optimizes PA locations using a Gauss-Seidel-based coordinate update with grid search under spacing constraints. Numerical results on MNIST and CIFAR-10 demonstrate that FedPASS achieves accuracy comparable to idealized FL baselines while drastically reducing the total training latency compared to conventional wireless FL.