Graphene provides an appealing platform to explore electronic analogs of optical effects due to the nonclassical nature of ballistic charge transport. Inspired by guiding of light in fiber optics, we demonstrate a means to guide the flow of electrons at the edges of a graphene crystal near charge neutrality. To visualize these states experimentally, we employ superconducting interferometry in a graphene Josephson junction and reconstruct the real-space supercurrent density using Fourier methods. To explain the observed behavior, we present a model that interprets the observed edge currents as guided-wave states, confined to the edge by natural band bending and transmitted as plane waves. At higher carrier densities, we also explore a new regime of superconducting transport in which Fabry-Perot interference of electron waves is a dominant feature. These results constitute a strong departure from conventional Josephson behavior and motivate further exploration of new effects at the intersection of superconductivity and electron-optics.