This paper investigates the performance of physical layer security (PLS) in fluid antenna-aided communication systems under arbitrary correlated fading channels. In particular, it is considered that a single fixed-antenna transmitter aims to send confidential information to a legitimate receiver equipped with a planar fluid antenna system (FAS), while an eavesdropper, also taking advantage of a planar FAS, attempts to decode the desired message. For this scenario, we first present analytical expressions of the equivalent channel distributions at the legitimate user and eavesdropper by using copula, so that the obtained analytical results are valid for any arbitrarily correlated fading distributions. Then, with the help of Gauss-Laguerre quadrature, we derive compact analytical expressions for the average secrecy capacity (ASC), the secrecy outage probability (SOP), and the secrecy energy efficiency (SEE) for the FAS wiretap channel. Moreover, for exemplary purposes, we also obtain the compact expression of ASC, SOP, and SEE by utilizing the Gaussian copula under correlated Rayleigh fading channels as a special case. Eventually, numerical results indicate that applying the fluid antenna with only one activated port to PLS can guarantee more secure and reliable transmission, when compared to traditional antenna systems (TAS) exploiting maximal ratio combining (MRC) and antenna selection (AS) under selection combining (SC).