Feynman variational path-integral theory was used to obtain the ground-state energy of a polaron in a quantum well in the presence of a Coulomb potential for arbitrary values of the electron-phonon coupling constant α. Numerical and analytical results showed that the energy shift was more sensitive to α than to the Coulomb binding parameter (β) and increased with the decrease of effective quantum well width lZ. It was interesting that due to the electronic confinement in the quasi-2D (quantum well) structures, the lower bound of the strong coupling regime was shifted to smaller values of α. Comparison of the polaron in the quantum well with that in the quantum wire or dot showed that the polaronic effect strengthened with decrease of the confinement dimension.