We report on the fabrication of hybrid molecular devices employing multi-layer graphene (MLG) flakes which are patterned with a constriction using a helium ion microscope or an oxygen plasma etch. The patterning step allows for the localization of a few-nanometer gap, created by electroburning, that can host single molecules or molecular ensembles. By controlling the width of the sculpted constriction, we regulate the critical power at which the electroburning process begins. We estimate the flake temperature given the critical power and find that at low powers it is possible to electroburn MLG with superconducting contacts in close proximity. Finally, we demonstrate the fabrication of hybrid devices with superconducting contacts and anthracene-functionalized copper curcuminoid molecules. This method is extendable to spintronic devices with ferromagnetic contacts and a first step towards molecular integrated circuits.