Quantum confinement is known to affect a nanosized superconductor through quantum-size variations of the electronic density of states; and due to electron-electron attraction, which can be enhanced due to quantum-confinement modifications of electronic wave functions. The superconducting correlations are strengthened by such quantum mechanical effect, in cooperation with relevant surface-substrate phonon interaction. The model calculations are in a reasonable agreement with experiments performed on high-quality aluminum films. Our findings shed light on the long-standing problem of size dependence of critical temperature in low-dimensional superconductors.