Fluorinated bioactive glasses (FBGs) combine the antibacterial properties of fluorine with the biological activity of phosphosilicate glasses. Because their biomedical application depends on the release of fluorine, the detailed characterization of the fluorine environment in FBGs is the key to understand their properties. Car-Parrinello molecular dynamics (CPMD) simulations have been performed on a 45S5 Bioglass composition in which 10 mol % of the CaO has been replaced with CaF2, and have allowed us to resolve some longstanding issues about the atomic structure of fluorinated bioglasses, with particular regard to the structural role of fluorine. F is coordinated almost entirely to the modifier ions Na and Ca, with a very small amount of residual Si-F bonds, whose fraction only becomes significant in the melt precursor. High temperature leads to Si-F bonds in both tetra-(SiO3F) and, less frequently, penta-coordinated (SiO4F and SiO3F2) complexes, showing that formation of these bonds through the expansion of the SiO4 coordination shell is generally less favored. There is no evidence for preferential bonding of F to either modifier ion: almost all F atoms are coordinated to both calcium and sodium in a "mixed state", rather than exclusively to either, as had been conjectured. We discuss the consequences of these findings on the properties of fluorine-containing bioglasses.