Nanocrystalline samples of Ba1-xCaxF2 prepared by high-energy milling show an unusually high F-ion conductivity, which exhibit a maximum in the magnitude and a minimum in the activation energy at x = 0.5. Here, we report an X-ray absorption spectroscopy (XAS) at the Ca and Sr K edges and the Ba L-3 edge and a molecular dynamics (MD) simulation study of the pure and mixed fluorides. The XAS measurements on the pure binary fluorides, CaF2, SrF2 and BaF2 show that high-energy ball-milling produces very little amorphous material, in contrast to the results for ball milled oxides. XAS measurements of Ba1-xCaxF2 reveal that for 0 < x < 1 there is considerable disorder in the local environments of the cations which is highest for x = 0.5. Hence the maximum in the conductivity corresponds to the composition with the maximum level of local disorder. The MD calculations also show a highly disordered structure consistent with the XAS results and similarly showing maximum disorder at x = 0.5.