The aim of this work is to use spin polarized density functional theory (DFT) to explore how functionalizing the periphery of FePc with F atoms affects its adsorption properties on reactive metals, specifically Rh and Ru. The results show that the interaction between FePc and the substrates is of chemisorption nature, which leads to a reduction in symmetry of the original four-fold rotational symmetry of FePc to C2 or lower. The symmetry reduction has a mixed electronic and geometric character, caused by the breakup of degenerate dxzanddyz orbitals, as well as the incommensurability between molecule and surface symmetries. Introducing fluorine to FePc weakens the interaction between the Ru (Rh) substrates and the organic part of the molecule, resulting in a C2 rotational symmetry reduction. Furthermore, this functionalization enhances the charge transfer to the molecule, which could be of interest to electronic applications.