This study investigates the impact of narrow-band terahertz pulses on the ferroelectric order parameter in Ba0.8Sr0.2TiO3 films on various substrates. The 375 nm thick BST film on an MgO (001) substrate exhibits enhanced THz-induced second harmonic generation when excited by THz pulses with a central frequency of 1.6 THz, due to the resonant excitation of the soft phonon mode. Conversely, the BST film on a Si (001) substrate shows no enhancement, due to its polycrystalline state. The 800 nm thick BST film on an MgO (111) substrate demonstrates maximum of second harmonic generation signal when excited by THz pulses at 1.8 THz, that is also very close to it`s soft mode frequency (1.9 THz). Notably, the frequency spectrum of the BST/MgO (111) film reveals peaks at both the fundamental and doubled frequencies, highlighting the quadratic dependence of SHG intensity on the THz pulse's electric field strength.