Massive connectivity with ultra-low latency and high reliability necessitates fundamental advances in future communication networks operating under finite-blocklength (FBL) transmission. Fluid antenna systems (FAS) have emerged as a promising enabler, offering superior spectrum and energy efficiency in short-packet/FBL scenarios. In this work, by leveraging the simplicity and accuracy of block-correlation channel modeling, we rigorously bound the performance limits of FBL-FAS from a statistical perspective, focusing on two key performance metrics: block error rate (BLER) and outage probability (OP). Furthermore, we introduce a novel complex-integral simplification method based on Gauss-Laguerre quadrature, which achieves higher approximation accuracy compared to existing Taylor-expansion-based approaches. Numerical results validate the robustness of the proposed analysis and clearly demonstrate the superiority of FBL-FAS over conventional multiple-antenna systems with fixed antenna placement.