We present PEGASE-HR, a new stellar population synthesis program generating high resolution spectra (R=10 000) over the optical range lambda=400--680 nm. It links the spectro-photometric model of galaxy evolution PEGASE.2 (Fioc & Rocca-Volmerange 1997) to an updated version of the ELODIE library of stellar spectra observed with the 193 cm telescope at the Observatoire de Haute-Provence (Prugniel & Soubiran 2001a). The ELODIE star set gives a fairly complete coverage of the Hertzprung-Russell (HR) diagram and makes it possible to synthesize populations in the range [Fe/H]=-2 to +0.4. This code is an exceptional tool for exploring signatures of metallicity, age, and kinematics. We focus on a detailed study of the sensitivity to age and metallicity of the high-resolution stellar absorption lines and of the classical metallic indices proposed until now to solve the age-metallicity degeneracy. Validity tests on several stellar lines are performed by comparing our predictions for Lick indices to the models of other groups. The comparison with the lower resolution library BaSeL (Lejeune et al. 1997) confirms the quality of the ELODIE library when used for simple stellar populations (SSPs) from 10 Myr to 20 Gyr. Predictions for the evolved populations of globular clusters and elliptical galaxies are given and compared to observational data. Two new high-resolution indices are proposed around the Hgamma line. They should prove useful in the analysis of spectra from the new generation of telescopes and spectrographs.