This paper presents an analytical framework for evaluating the coverage performance of the fluid antenna system (FAS)-enhanced LoRa wide-area networks (LoRaWANs). We investigate the effects of large-scale pathloss in LoRaWAN, small-scale fading characterized by FAS, and dense interference (i.e., packet collisions under the ALOHA protocol) arising from randomly deployed end devices (EDs). Both co-spreading factor (co-SF) interference (with the same SF) and inter-SF interference (with different SFs) are introduced into the network, and their differences in physical characteristics are also considered in the analysis. Additionally, simple yet accurate statistical approximations of the FAS channel envelope and power are derived using the extreme-value theorem. Based on the approximated channel expression, the theoretical coverage probability of the proposed FAS-enhanced LoRaWAN is derived. Numerical results validate our analytical approximations by exhibiting close agreement with the exact correlation model. Notably, it is revealed that a FAS with a normalized aperture of 1 times 1 can greatly enhance network performance, in terms of both ED numbers and coverage range.