Aims. A variation of the fundamental constants is expected to affect the thermonuclear rates important for stellar nucleosynthesis. In particular, because of the very low resonant energies of ⁸Be and ¹²C, the triple α process is extremely sensitive to any such variations. Methods. Using a microscopic model for these nuclei, we derive the sensitivity of the Hoyle state to the nucleon-nucleon potential, thereby allowing for a change in the magnitude of the nuclear interaction. We follow the evolution of 15 and 60 Mʘ zero-metallicity stellar models, up to the end of core helium burning. These stars are assumed to be representative of the first, Population III stars. Results. We derive limits on the variation in the magnitude of the nuclear interaction and model dependent limits on the variation of the fine structure constant based on the calculated oxygen and carbon abundances resulting from helium burning. The requirement that some ¹²C and ¹⁶O be present at the end of the helium burning phase allows for permille limits on the change in the nuclear interaction and limits of the order of 10⁻⁵ on the fine structure constant relevant at a cosmological redshift of z ∼ 15−20.