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 (FrAg)-Fr-223-Ag-107 molecule, as the octupole deformation of the unstable Fr-223 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, Fr-223 atoms and Ag-107 atoms have to be brought together at ultracold temperatures. That is, we explore the prospects of forming (FrAg)-Fr-223-Ag-107 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 Fr-223 + Ag-107 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 (FrAg)-Fr-223-Ag-107 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.