Free-surface fluid simulations play an essential role both in engineering applications and natural phenomena. They treat scenarios where the fluid interface moves freely without constraints. While the initial configuration of the interface is usually known, its temporal evolution must be computed as part of the solution, often resulting in complex, transient geometries that are challenging for numerical approaches. Lagrangian methods have proven particularly effective for these simulations as they naturally track interface position and evolution. However, mesh-based Lagrangian approaches frequently suffer from deteriorating mesh quality as nodes move over time. The Particle Finite Element Method (PFEM) addresses this limitation by combining a Finite Element solver with an efficient remeshing technique that maintains mesh quality throughout the simulation process. While PFEM effectively handles complex problems, it demands significant computational resources. Surrogate models could offer faster alternatives by approximating system behaviour, but developing classical Reduced Order Models (ROMs) for PFEM presents unique challenges. Unlike traditional approaches where data exists on fixed meshes, PFEM simulations operate on successive unstructured meshes, making it difficult to establish a reference configuration for bijective mapping. Recent Deep Learning advances offer promising solutions through Neural Network-based data-driven models, capable of identifying complex patterns and potentially achieving real-time simulations. We propose NeuralPFEM(NPFEM) model, that combines a Lagrangian neural simulator with PFEM's efficient remeshing procedure. NPFEM maintains the structure of the original PFEM but computes solution fields at each time step using an autoregressive neural solver built on an Encoder-Processor-Decoder architecture. This framework transforms input data into a latent space that captures hidden patterns, processes it in this abstract representation, and then maps it back to its original form. Unlike other state-of-the-art particle-based surrogate models, NPFEM generates output on time-evolving meshes, offering several advantages such as enhanced postprocessing capabilities and a more uniform particle distribution that mitigates particle clustering issues. Moreover, by preserving PFEM's temporal and spatial discretization, NPFEM ensures strong compatibility with the original model, an essential feature for developing hybrid methods that combine