Enzymatic reduction of CO₂ to formic acid with the enzyme formate dehydrogenase (FDH) and a cofactor is a promising method for CO₂ conversion and utilization. However, the natural cofactor nicotinamide adenine dinucleotide (NADH) shows some drawbacks such as a low reduction efficiency and forms isomers or dimers (1,6 - NADH or NAD dimer) in the regeneration reaction. To overcome them and to improve the production of formic acid, in this work, the artificial cofactors, i.e., the bipyridinium-based salts of methyl viologen (MV²⁺), 1,1’-dicarboxymethyl-4,4’-bipyridinium bromine (DC²⁺), and 1,1’-diaminoethyl-4,4’-bipyridinium bromine (DA²⁺), were used to replace NADH, and the effect of different functional groups on the electrochemical regeneration and catalytic performance in the enzymatic reaction was studied systematically. Also, studies using the natural cofactor NADH were carried out for comparison. It was found that the cofactor with amino groups showed the highest catalytic efficiency (k_cat/K_m) of 0.161 mM^-1min^-1, which is 536 times higher than that of the natural cofactor NADH. Molecular Dynamics simulations were conducted to give further molecular insight into the behavior of the cofactors. Analyzing the free energy profiles of the complexes between CO₂ in the FDH active site with different artificial cofactors indicated that the artificial cofactor with the amino groups had the highest affinity for CO₂, being consistent with the experimental observations.