We employed first-principles calculations to investigate the fluorination of silicon carbide nanosheets. We found that the Si atoms are the energetically favorable adsorption sites for F atoms in silicon carbide nanosheets in all studied cases. The strain caused by the fourfold coordinated Si atoms in the flat SiC nanosheet determines the relative position of the adsorbed F atoms: occupying nearest-neighbor Si sites if they bound sheet’s opposing sides or away from each other if they are on the same side of the sheet. The fluorinated nanosheets’ electronic and magnetic properties are weakly dependent on which side of the sheet the F atoms bind; however, they are strongly dependent on the relative distance between them. For F atoms adsorbed on nearest-neighbor Si sites, the system is a small gap p-type semiconductor with 1 μB per adsorbed atom. On the other hand, if F atoms do not occupy nearest-neighbor Si sites, the system is a metal with 1/2 μB per adsorbed atom. The adsorption of F atoms strongly affects the optical properties of SiC sheets inducing optical anisotropy regarding the direction of the incidence of light.