Picosecond laser ultrasonics is an experimental technique for the generation and detection of ultrashort acoustic pulses using ultrafast lasers. In transparent media, it is often referred to as time-domain Brillouin scattering (TDBS). It provides the opportunity to monitor the propagation of nanometers-length acoustic pulses and to determine acoustical, optical, and acousto-optical parameters of the materials. We report on the application of TDBS for evaluating the effect of Praseodymium (Pr) substitution on the elasticity of multiferroic (Bi1−xPrx)(Fe0.95Mn0.05)O3 (BPFMO) thin films. The films were deposited on Si and LaAlO3 (LAO) substrates by a sol-gel method. X-ray diffraction and Raman spectra revealed earlier that a phase transition from rhombohedral to tetragonal structure occurs at about 15% Pr substitution and is accompanied by the maxima of remnant magnetization and polarization. Combining TDBS with optical spectral reflectometry, scanning electron microscopy, and topographic measurements by atomic force microscopy, we found that the structural transition is also characterized by the maximum optical dielectric constant and the minimum longitudinal sound velocity. Our results, together with earlier ones, suggest that BiFeO3-based films and ceramics with compositions near phase boundaries might be promising materials for multifunctional applications.