  Epitaxial semiconductor-superconductor heterostructures are promising as a
platform for gate-tunable superconducting electronics. Thus far, the
superconducting properties in such hybrid systems have been predicted based on
simplified hybridization models which neglect the electronic structure that can
arise at the interface. Here, we demonstrate that the hybrid electronic
structure derived at the interface between semiconducting black phosphorus and
atomically thin films of lead can drastically modify the superconducting
properties of the thin metallic film. Using ultra-low temperature scanning
tunneling microscopy and spectroscopy, we ascertain the moir\'e structure
driven by the interface, and observe a strongly anisotropic renormalization of
the superconducting gap and vortex structure of the lead film. Based on density
functional theory, we attribute the renormalization of the superconductivity to
weak hybridization at the interface where the anisotropic characteristics of
the semiconductor band structure is imprinted on the Fermi surface of the
superconductor. Based on a hybrid two-band model, we link this
hybridization-driven renormalization to a weighting of the superconducting
order parameter that quantitatively reproduces the measured spectra. These
results illustrate the effect of interfacial hybridization at
superconductor-semiconductor heterostructures, and pathways for engineering
quantum technologies based on gate-tunable superconducting electronics.
