Stable and metastable atomic configurations of stoichiometric (LaF3)n nanoclusters are obtained for n = 1 to 6 using Monte Carlo global optimization techniques implemented in newly developed software. All configurations are refined using an all-electron DFT approach with the PBEsol exchange and correlation functional. To reduce the computational cost, approximate configurations were initially filtered out using a basin hopping algorithm that was biased toward finding either the global minimum or all metastable minima on the six energy landscapes defined by interatomic potentials within a polarizable shell model. In both algorithms, standard local optimization methods are employed to relax trial random atomic configurations whereby the polarization of the ions is initially constrained to improve convergence to local energy minima. The global optimization routines were implemented within the in-house Knowledge Led Master Code (KLMC). Electronic characterization of the refined structures included the calculation of vertical ionization potentials and electron affinities using the ΔSCF approach at the PBEsol DFT level and the many-body G0W0/PBEsol0 theory which employs the hybrid density functional initial guess of the quasi-particle orbitals. The atomic structure of the nanoclusters can be seen to evolve with size from a trigonal pyramid to ring structures and finally to compact symmetrical configurations, where the coordination of higher charged La gradually increases. Additional fluorine ions are accommodated between two La ions: single fluoride (−F−) bridges are replaced by bridge pairs or trios, although more than three fluoride bridges between two cations are heavily penalized in energy and cluster ranking. There is also a trend for the external surface of LaF3 nanoclusters to be decorated by singly coordinated fluorine anions, one per outer La ion for larger nanoclusters. For the global minimum (LaF3)n nanoclusters, although the changes are modest, the ionization potential decreases, and the electron affinity increases with n, effectively decreasing the precursor of the band gap of the bulk phase. The majority of the metastable nanoclusters follows this trend, with the exception of configurations with at least one exposed cation at the surface which is not terminated by an anion. These nanoclusters have a greater electron affinity that could be attributed to structural features analogous to defects in solids.