We investigate supercurrent interference patterns measured as a function of magnetic field in ballistic graphene Josephson junctions. At high doping, the expected φ0-periodic "Fraunhofer"pattern is observed, indicating a uniform current distribution. Close to the Dirac point, we find anomalous interferences that are close to a 2φ0 periodicity, similar to that predicted for topological Andreev bound states carrying a charge of e instead of 2e. This feature persists with increasing temperature, ruling out a nonsinusoidal current-phase relationship. It also persists in junctions in which sharp vacuum edges are eliminated. Our results indicate that the observed behavior may originate from an intrinsic property of ballistic graphene Josephson junctions, though the exact mechanism remains unclear.