The exponents of spin and charge correlations of one-dimensional electron systems are calculated by a renormalization-group method. We study combined effects of electron-phonon interaction and the Umklapp process on renormalization flows. As scattering processes are successively integrated out, these two processes are interfered with each other depending on the type of electron-phonon coupling, phonon frequency and filling. We demonstrate how these factors control a spin gap formation and density-wave/superconductor correlations.