The energy relaxation of the electrons in the conduction band of 12 and 30 nm diameter copper nanoparticles in colloidal solution was investigated using femtosecond time-resolved transient spectroscopy. Experimental results show that the hot electron energy relaxation is faster in 12 nm copper nanoparticles (0.37 ps) than that in 30 nm copper nanoparticles (0.51 ps), which is explained by the size-dependent electron-surface phonon coupling. Additional mechanisms involving trapping or energy transfer processes to the denser surface states (imperfection) in the smaller nanoparticles are needed to explain the relaxation rate in the 12 nm nanoparticles. The observed fluorescence quantum yield from these nanoparticles is found to be enhanced by roughly 5 orders of magnitude for the 30 nm nanoparticles and 4 orders of magnitude for the 12 nm nanoparticles (relative to bulk copper metal). The increase in the fluorescence quantum yield is attributed to the electromagnetic enhancement of the radiative recombination of the electrons in the s-p conduction band below the Fermi level with the holes in the d bands due to the strong surface plasmon oscillation in these nanoparticles.