The novel ZrIV-based PerFluorinated Metal-Organic Framework (PF-MOF) [Zr6O4(OH)4(TFS)6] (ZrTFS) was prepared under solvent-free conditions using the commercially available tetrafluorosuccinic acid (H2TFS) as bridging ditopic linker. Since H2TFS can be seen as the fully aliphatic and perfluorinated C4 analogue of fumaric acid, ZrTFS was found to be isoreticular to zirconium fumarate (MOF-801). The structure of ZrTFS was solved and refined from X-ray Powder Diffraction data. Despite this analogy, the gas adsorption capacity of ZrTFS is much lower than that of MOF-801; in the former, the presence of bulky fluorine atoms causes a considerable windows size reduction. In order to have PF-MOFs with more accessible porosity, Post-Synthetic Exchange (PSE) reactions on (defective) MOF-801 suspended in H2TFS aqueous solutions were carried out. Despite the different H2TFS concentrations used in the PSE process, the exchanges yielded two mixed-linker materials of similar minimal formulae [Zr6O4(μ3-OH)4(μ1-OH)2.08(H2O)2.08(FUM)4.04(HTFS)1.84] (PF-MOF1) and [Zr6O4(μ3-OH)4(μ1-OH)1.83(H2O)1.83(FUM)4.04(HTFS)2.09] (PF-MOF2) (FUM2- = fumarate), where the perfluorinated linker was found to fully replace the capping acetate in the defective sites of pristine MOF-801. CO2 and N2 adsorption isotherms collected on all samples reveal that both CO2 thermodynamic affinity (isosteric heat of adsorption at zero coverage, Qst) and CO2/N2 adsorption selectivity increase with the amount of incorporated TFS2-, reaching the maximum values of 30 kJ mol-1 and 41 (IAST), respectively, in PF-MOF2. This confirms the beneficial effect coming from the introduction of fluorinated linkers in MOFs on their CO2 adsorption ability. Finally, solid-state density functional theory calculations were carried out to cast light on the structural features and on the thermodynamics of CO2 adsorption in MOF-801 and ZrTFS. Due to the difficulties in modelling a defective MOF, an intermediate structure containing both linkers in the framework was also designed. In this structure, the preferential CO2 adsorption site is the tetrahedral pore in the “UiO-66-like” structure. The extra energy stabilization stems from a hydrogen bond interaction between CO2 and a hydroxyl group on the inorganic cluster.