In this article, we report our development of a vibronic model for the electric-field control of antiferromagnetic superexchange in the mixed-valence (MV) triferrocenium complex Fe^III-Fe^II-Fe^III proposed as a possible candidate for the molecular implementation of a quantum logic gate. Along with the electronic interactions, such as electron transfer between the iron ions in different oxidation degrees and Coulomb repulsion of the extra holes, the proposed model of the triferrocenium complex also takes into account the vibronic coupling as an inherent ingredient of the problem of mixed valency. The latter is described by the conventional Piepho-Krauzs-Shatz (PKS) model adapted to the linear disposition of the redox sites in the trimeric Fe^III-Fe^II-Fe^III complex, which gives a clear insight into the degree of delocalization in mixed-valence compounds. By introducing symmetry adapted molecular vibrations composed of the local "breathing" displacements, the three-mode vibronic problem is reduced to a two-mode problem involving interaction with the even and odd molecular vibrations of the linear centrosymmetric complex. The vibronic coupling was shown to play a key role in the degree of localization of the two holes among the three iron centers. This was shown to produce a pronounced influence on the electric-field dependences of the electronic-density distributions and electrically switchable magnetic exchange in the considered linear triferrocenium complex. In particular, it was shown that the vibronic coupling significantly influences the field-induced stepwise transformation Fe^III-Fe^II-Fe^III ↔ Fe^III-Fe^III-Fe^II, increasing the abruptness of the field dependencies of the singlet-triplet gap and the hole densities, which are of primary importance for the switching function.