Low Reynolds complex fluid dynamics problems, such as free-surface fluid flows, are of great interest for the simulation of a wide range of engineering applications and natural phenomena. The main computational challenge lies in the need to simultaneously compute both the evolution of the solution and the interface over time. The Particle Finite Element Method (PFEM) has proven to be ideal for solving such problems as the Lagrangian nature of the solver naturally captures the evolution of the interface. The method is based on a fluid finite element solver combined with efficient re-meshing algorithms. However, despite its strengths, PFEM remains limited by its computational cost—particularly for large-scale simulations or when exploring extensive parameter spaces. To alleviate this, Model Order Reduction (MOR) can be employed to significantly reduce the computational time. It relies on the construction of a reduced solution manifold and the projection of the governing equations onto this manifold, thereby solving a much smaller system. Nevertheless, adapting MOR to PFEM presents notable challenges. The most important is that the data in PFEM simulations is not defined on a fixed mesh, this makes it difficult to compute the solution manifold as well as the reference configuration on which the information can be mapped. Regarding the exact reduction method, we opt for the Proper Generalized Decomposition which does not require any knowledge of past solutions to construct the reduced manifold. Instead, we alternate between iteratively solving problems of lower dimensions to calculate the reduced solution fields and recalculating the Lagrangian meshes from the full velocity field. Convergence is reached when the mesh velocity matches the fluid velocity. This approach can naturally be extended to multi-parametric scenarios, enabling efficient exploration of parameter spaces without the need for repeated full-order simulations.