Electron phonon (el-ph) coupling is a fundamental quantity that controls the electron transport through a conductor. We experimentally determined the el-ph coupling strength of epitaxial copper (Cu) films ranging from 5 to 1000 nm thick using both ultra-fast, optical pump-probe reflectivity and temperature-dependent resistivity measurements. An enhancement of the el-ph coupling strength was observed when the thickness of the films was reduced to below 50 nm. We suggest that this unexpected enhancement of the el-ph coupling strength is partially responsible for the observed increase of resistivity in the films below 50 nm thick.