This study is devoted to the problem of the electron-vibrational interaction in 4f-5d optical transitions. We analyze the room temperature experimental data on the vibronically assisted broad bands arising from the 4f-5d transitions in Ba, Ca, and Sr thiogallates doped with Eu²⁺ ions. An approximate simple expression is given for the shape function of the broad vibronic bands with allowance for the terms corresponding to the emission (absorption) from both ground and first excited vibrational levels. We estimate the vibronic coupling parameters and the Stokes shifts for these systems. The theoretical results are in a good agreement with the experimental data.