A new approach to creating a new and locally nanostructured graphene-based material is reported. We studied the electric and structural properties of partially fluorinated graphene (FG) films obtained from an FG-suspension and nanostructured by high-energy Xe ions. Local shock heating in ion tracks is suggested to be the main force driving the changes. It was found that ion irradiation leads to the formation of locally thermally expanded FG and its cracking into nanoparticles with small (∼1.5-3 nm) graphene quantum dots (GQD), embedded in them. The bandgap of GQD was estimated as 1 -1.5 eV. A further developed approach was applied to correct the functional properties of printed FG-based crossbar memristors. Dielectric FG films with small quantum dots may offer prospects in graphene-based electronics due to their stability and promising properties.