Solvothermal reactions of Cu(NO3)(2) center dot 3H(2)O with 4,4'-(hexafluoroisopropylidene) bis(benzoic acid) (C17H10F6O4, H(2)hfbba) and terminal monodentate ligand 3-methyl pyridine (3-picoline/3-mepy) in the presence of N, N-dimethyl formamide (DMF) and N,N-diethyl formamide (DEF) solvents gave rise to two structurally different two-dimensional (2D) fluorinated metal organic frameworks (F-MOFs). The effect of the choice of solvent has been clearly reflected in the structures obtained. The F-MOFs reported in this paper are formulated as [Cu-2(hfbba)(2)(3-mepy)(2)] center dot (DMF)(2)(3-mepy) (F-MOF-4), [Cu-2(hfbba)(2)(3-mepy)(2)] (Cu-F-MOF-4B), and [Zn-2(hfbba)(2)(3-mepy)(2)] center dot (3-mepy) (Zn-F-MOF-4B) which displays interesting 2D structures with and without interdigitation depending on the solvent used. The structures of these F-MOFs have been determined by X-ray crystallography and further identified by IR spectroscopy, powder X-ray diffraction (PXRD), and thermogravimetric analysis (TGA). The effect of interdigitation has been reflected in the gas adsorption and magnetic properties of these F-MOFs. These F-MOFs also show comparable H-2 and CO2 uptake depending on their structural variation. Temperature-dependent magnetic susceptibility measurements over a wide range of temperatures exhibit dominantly short-range antiferromagnetic behavior, with weak ferromagnetic behavior showing up at very low temperatures, which is evident from opening of the hysteresis loop with a finite value of coercivity in both F-MOF-4 and Cu-F-MOF-4B. We observed a smaller value of mu(eff) per Cu atom and coercivity in Cu-F-MOF-4B than the F-MOF-4 due to relatively larger distances between the neighboring dicopper paddlewheel secondary building unit.