A polarizable ionic interaction potential, constructed from first-principles calculations, is used to examine the structure, vibrational spectra, and transport properties of molten mixtures of LiF and BeF2 across a range of compositions. The simulations reproduce the experimentally measured vibrational frequencies of the fluoroberyllate (BeF4(2-)) ions, which form in the melt, as well as conductivity and viscosity values across the composition range. Examination of the structures of the melts reveals the emergence of a slowly relaxing network of BeF4 units as the concentration of BeF2 is increased. The relationship between the appearance of the network and the composition dependence of the transport properties is explored.