  We show that the coupling to vibrational degrees of freedom can drive a
semimetal excitonic-insulator quantum phase transition in an one-dimensional
two-band f-c electron system at zero temperature. The insulating state typifies
an excitonic condensate accompanied by a finite lattice distortion. Using the
projector-based renormalization method we analyze the ground-state and spectral
properties of the interacting electron-phonon model at half-filling. In
particular we calculate the momentum dependence of the excitonic order
parameter function and determine the finite critical interaction strength for
the metal-insulator transition to appear. The electron spectral function
reveals the strong hybridization of f- and c-electron states and the opening of
a single-particle excitation gap. The phonon spectral function indicates that
the phonon mode involved in the transition softens (hardens) in the adiabatic
(non-adiabatic and extreme anti-adiabatic) phonon frequency regime.
