Context. Nova 1670 is a historical transient bearing strong similarities to a recently recognized type of stellar eruption known as the red nova, which is thought to be powered by stellar mergers. The remnant of the transient, CK Vul, is observable today mainly through cool circumstellar gas and dust, and recombining plasma, but we have no direct view on the stellar object. Aims. Within the merger hypothesis, we aim to infer the most likely configuration of the progenitor system that resulted in Nova 1670. Methods. We collected the literature data on the physical properties of the outburst and the remnant (including their energetics), and on the chemical composition of the circumstellar material (including elemental and isotopic abundances). These data, which result from optical and submillimeter observations of the circumstellar gas of CK Vul, are summarized here. We performed simple simulations to analyze the form and the level of mixing within the material associated with the merger. We identified products of nuclear burning, among which we find ashes of hydrogen burning in the CNO cycles and in the MgAl chain, as well as signs of partial helium burning. Results. Based primarily on the luminosity and chemical composition of the remnant, we find that the progenitor primary had to be an evolutionarily advanced red giant branch star of a mass of 1–2 M⊙. The secondary was either a very similar giant, or –more likely– a helium white dwarf. While the eruption event was mainly powered by accretion, we estimate that about 12% of total energy is likely to have come from helium burning activated during the merger. The coalescence of a first-ascent giant with a helium white dwarf created a star with a rather unique internal structure and composition, which resemble those of early R-type carbon stars. Conclusions. Nova 1670 is the result of a merger between a helium white dwarf and a first-ascent red giant and is likely now evolving to become an early R-type carbon star.