CK Vulpeculae or Nova 1670 is an enigmatic eruptive object which underwent a stellar-merger event recorded by seventeenth-century observers. Its remnant was recently recovered at submillimeter wavelengths, revealing gas of an extraordinary isotopic composition indicative of past processing in the CNO cycles and partial He burning. Here, we present long-slit optical spectra of the remnant acquired with X-shooter at the Very Large Telescope (VLT) at an unprecedented sensitivity and spectral coverage. The spectra cover features of key elements, including H, He, C, N, and O, at ionization degrees I-III. A classical analysis of the spectra allowed us to identify several spatio-kinematic components in the probed part of the nebula at electron temperatures of 10-15 kK and densities of 200-600 cm(-3). We find that the nebula is most likely excited by shocks rather than by direct radiation of the stellar remnant. We provide a detailed analysis of the elemental abundances in the remnant and find that helium is two times more abundant than in the Sun. Nitrogen is also overabundant with a N/O ratio ten times larger than the solar one. These anomalous abundances strongly indicate that the observed gas was processed in CNO cycles of H burning, consistent with the submillimeter studies. Additionally, sub-solar abundances of heavier elements, such as Ne, S, and Ar, suggest that the progenitor of CK Vul was formed from material poorer in metals than the Sun and was, therefore, an old stellar system before the 1670 eruption.