Molecules with unstable isotopes often contain heavy and deformed nuclei and thus possess a high sensitivity to parity-violating effects, such as the Schiff moments. Currently the best limits on Schiff moments are set with diamagnetic atoms. Polar molecules with quantum-enhanced sensing capabilities, however, can offer better sensitivity. In this work, we consider the prototypical 223 Fr 107 Ag molecule, as the octupole deformation of the unstable 223 Fr francium nucleus amplifies the nuclear Schiff moment of the molecule by two orders of magnitude relative to that of spherical nuclei and as the silver atom has a large electron affinity. To develop a competitive experimental platform based on molecular quantum systems, 223 Fr atoms and 107 Ag atoms have to be brought together at ultracold temperatures. That is, we explore the prospects of forming 223 Fr 107 Ag from laser-cooled Fr and Ag atoms. We have performed fully relativistic electronic-structure calculations of ground and excited states of FrAg that account for the strong spin-dependent relativistic effects of Fr and the strong ionic bond to Ag. In addition, we predict the nearest-neighbor densities of magnetic-field Feshbach resonances in ultracold 223 Fr+ 107 Ag collisions with coupled-channel calculations. These resonances can be used for magneto-association into ultracold, weakly-bound FrAg. We also determine the conditions for creating 223 Fr 107 Ag molecules in their absolute ground state from these weakly-bound dimers via stimulated Raman adiabatic passage using our calculations of the relativistic transition electric dipole moments.