The present work aims to shed light on the extent to which the structural self-organizationSelf-organization of chalcogenide glasses influences the low-frequency Raman scattering (Boson peakBoson peak), while seeking the relevant reasons for this phenomenon. For this purpose, a number of both stoichiometric and non-stoichiometric sulfurous glasses based on As and Ge from the intermediate phase with a beforehand established degree of self-organizationSelf-organization were considered. The Raman measurements were performed between 10 and 250 cm−1; however, only the low-frequency spectral range (10–125 cm−1) was carefully analyzed in relation to the results of XRD and ultrasonic wave propagation experiments. It was pointed out that the spectral position of the Boson peakBoson peak (BP) correlates with the size of fractal domains in the medium-range order structure of the glass, while its intensity depends on both material stoichiometry and composition, diminishing with an increase in Ge concentration. Calculation of the excess of the vibrational density of states (e-VDOS) over the counterpart density Debye of vibrations (DV) at BP has shown its gradual decrease with increasing Ge concentration, tending to zero at compositions with the maximum degree of organization (7–10 at% Ge). In more germanium-rich glasses, the DV prevails, and Raman scattering depends only on the value of the photon-vibration coupling constant C (ω) of the glass.