The Particle Finite Element method is a fluid solver based on Lagrangian finite elements combined with efficient re-meshing algorithms [1]. It was shown to be effective in a large amount of applications, especially in the case of free surface fluids flows or fluid-structure interactions. Up to now, this method has never been paired up with any model-order reduction technique because of the difficulties linked to the re-meshing schemes. In this work, we mainly focus on an a priori reduction method called Proper Generalized Decomposition (PGD) [2] with a space-time decomposition. To build the reduced model, the PGD does not require any knowledge of past solutions. This technique has been used before in the context of Eulerian finite element fluid solvers [3] but the performance improvement was limited by the non-linear convective term. This justifies the hopes we have to be able to solve higher convective cases with the Lagrangian approach, where the convective term entirely vanishes. The PGD formulation requires a complete time integration of all points of our system. To be able to deal with moving mesh and remeshing, a new expanded formulation is introduced. Particular efforts have to be made to ensure both correct mesh and solution interpolation at the re-meshing instances and adequate update of the mesh after every new mode calculation. The proposed technique has been validated with simple tests showing very promising results.