The conductivity of few- and monolayer graphene with covalently bound moieties is a key-point in the potential application of these materials in any electrical and optoelectronic device. In particular, fluorination of such graphene-based systems is of interest, as fluorine is expected to have a strong influence on the charge-carrier density due to its high electronegativity, and therefore modify the electrical transport properties significantly. Here it is shown that, depending on the device architecture, the electrical properties of fluorinated graphene-based devices are significantly different. It is found that the conductivity of thin films of few-layer graphene decreases by several orders of magnitude with fluorine content increasing from 2.4 to 16.6 at%, whereas individual flakes show a significant increase in both conductivity and charge carrier mobility. This observation, combined with Raman microscopy study, points toward the fact that the edges of the flakes are primary sites for fluorine within the experimental range of fluorine content. The strong decrease in conductivity in the film devices is therefore associated with the high contact resistance between the fluorine saturated edges of the individual flakes.