Copper(II) complexes with a general formula [Cu2(3,4-F2C6H3CH2COO)4(L)2], where L = 2-methylpyridine (1) and 3-methylpyridine (2), are reported here. The FTIR spectra of the complexes confirmed the bridging bidentate coordination mode of the carboxylate ligand. The low (475 and 449 cm−1) and strong (727 & 725 cm−1) intensity bands in the FTIR spectra, due to Cu-N stretches and pyridyl ring vibrations, confirmed coordination of the 2-/3-methyl pyridine co-ligands in complexes 1 and 2, respectively. A binuclear paddlewheel structural arrangement with a square pyramidal geometry was confirmed for copper atoms in the complexes via single-crystal X-ray analysis. The DPPH, •OH radical, and α-amylase enzyme inhibition assays showed higher activities for the complexes than for the free ligand acid. The binding constant (Kb = 1.32 × 105 for 1 and 5.33 × 105 for 2) calculated via UV-VIS absorption measurements and docking scores (−6.59 for 1 and −7.43 for 2) calculated via molecular docking showed higher SS-DNA binding potential for 2 compared to 1. Viscosity measurement also reflected higher DNA binding ability for 2 than 1. Both complexes 1 and 2 (docking scores of −7.43 and −6.95, respectively) were found to be more active inhibitors than the free ligand acid (docking score of −5.5159) against the target α-amylase protein. This in silico study has shown that the herein reported compounds follow the rules of drug-likeness and exhibit good potential for bioavailability.