The accurate simulation of free-surface fluid flows is essential in many engineering and geophysical applications, where the fluid interface evolves freely and may undergo large deformations. Capturing such highly transient and complex geometries poses significant numerical challenges. Among the available techniques, Lagrangian methods are particularly well suited for tracking free surfaces, as they naturally describe the motion of interfaces. In this context, the Particle Finite Element Method (PFEM) has proven effective by combining a finite element solver with continuous remeshing strategies that preserve mesh quality throughout the simulation. Despite its robustness, PFEM remains computationally expensive, motivating the development of reduced-order and surrogate models. However, applying model order reduction techniques to PFEM is non-trivial due to the absence of a fixed reference mesh, which complicates the definition of a solution manifold and the mapping of data across successive unstructured meshes. In this work, we propose a novel reduced-order modeling strategy based on Proper Generalized Decomposition (PGD) tailored for non-constant computational domains with mesh motion and remeshing. The method alternates between solving reduced, lower-dimensional problems to compute the solution fields and updating the Lagrangian mesh using the full velocity field. Convergence is achieved when the mesh velocity coincides with the fluid velocity. The proposed framework naturally extends to multi-parametric problems, enabling efficient exploration of parameter spaces without the need for repeated full-order PFEM simulations.