We compute the free energy minimizing structures of particle monolayers in the presence of enthalpic barriers of a finite height βV(ext) using classical density functional theory and Monte Carlo simulations. We show that a periodic square template with dimensions up to at least 10 times the particle diameter disrupts the formation of the entropically favored hexagonally close-packed 2D lattice in favor of a square lattice. The results illustrate how graphoepitaxy can successfully order nanoparticulate films into desired patterns many times smaller than those of the prepatterned template.