We show that Cs intercalated bilayer graphene acts as a substrate for the growth of a strained Cs film hosting quantum well states with high electronic quality. The Cs film grows in an fcc phase with a substantially reduced lattice constant of 4.9 Å corresponding to a compressive strain of 11% compared to bulk Cs. We investigate its electronic structure using angle-resolved photoemission spectroscopy and show the coexistence of massless Dirac and massive Schrödinger charge carriers in two dimensions. Analysis of the electronic self-energy of the massive charge carriers reveals the crystallographic direction in which a two-dimensional Fermi gas is realized. Our work introduces the growth of strained metal quantum wells on intercalated Dirac matter.