The magnetic ground state of EuC₆, a first-stage graphite intercalation compound, was investigated by means of zero-field muon spectroscopy. Below the Néel antiferromagnetic temperature (42 K), the highly damped oscillations in the muon asymmetry could be modelled with a Bessel line shape, indicative of an incommensurate magnetic order. The internal magnetic field, as probed by the implanted muons, lies in the plane of the europium ions, has an average intensity of 150(22) mT, and seems to arise from a strong contact hyperfine interaction. The latter partially cancels out the dipolar contribution to the local field, in turn due to the localized Eu spins arranged in an antiferromagnetic triangular lattice (frustrated spin lattice) with negligible inter-layer couplings.