We propose that chemically inert polymeric films can enhance van der Waals (vdW) forces in the same way as nanofabrication of biomimetic adhesive materials. For the vdW adhesion of an ethylene-chlorotrifluoroethylene (ECTFE) film on rough metal and dielectric substrates, we present a model that combines microscopic quantum-chemistry simulations of the polymer response functions and the equilibrium monomer-substrate distance with a macroscopic quantum-electrodynamics calculation of the Casimir force between the polymer film and the substrate. We predict adhesive forces up to 2.22 kN/mm2, where the effect is reduced by substrate roughness and for dielectric surfaces.