We report on a ballistic and fully tunable Josephson-junction system consisting of two parallel ribbons of graphene in contact with superconducting molybdenum-rhenium. By electrostatic gating of the two individual graphene ribbons, we gain control over the real-space distribution of the superconducting current density, which can be continuously tuned between the two ribbons. We extract the respective gate-dependent spatial distributions of the real-space current density by employing Fourier and Hilbert transformations of the magnetic-field-induced modulation of the critical current. This approach is fast and does not rely on a symmetric current profile. It is therefore a universally applicable tool, potentially useful for carefully adjusting Josephson junctions.