Magnetic and superconducting interactions couple electrons together to form complex states of matter. We show that, at the atomic scale, both types of interactions can coexist and compete to influence the ground state of a localized magnetic moment. Local spectroscopy at 4.5 kelvin shows that the spin-1 system formed by manganese-phthalocyanine (MnPc) adsorbed on Pb(111) can lie in two different magnetic ground states. These are determined by the balance between Kondo screening and superconducting pair-breaking interactions. Both ground states alternate at nanometer length scales to form a Moiré-like superstructure. The quantum phase transition connecting the two (singlet and doublet) ground states is thus tuned by small changes in the molecule-lead interaction.