Since the early days of quantum mechanics, it has been known that electrons behave simultaneously as particles and waves, and now quantum electronic devices can harness this duality. When devices are shrunk to the molecular scale, it is unclear under what conditions does electron transmission remain phase-coherent, as molecules are usually treated as either scattering or redox centers, without considering the wave-particle duality of the charge carrier. Here, we demonstrate that electron transmission remains phase-coherent in molecular porphyrin nanoribbons connected to graphene electrodes. The devices act as graphene Fabry-Pérot interferometers and allow for direct probing of the transport mechanisms throughout several regimes. Through electrostatic gating, we observe electronic interference fringes in transmission that are strongly correlated to molecular conductance across multiple oxidation states. These results demonstrate a platform for the use of interferometric effects in single-molecule junctions, opening up new avenues for studying quantum coherence in molecular electronic and spintronic devices.