The pressure dependence of various inter- and intra-layer Raman modes has been studied on pristine matlockite compound, PbFCl, up to ~41 GPa. The low-frequency interlayer vibrational modes, A1g(1) and Eg(1), identified as rigid layer modes, exhibit non-monotonic behavior with increasing pressure. They exhibit points of inflexion at ~24 GPa and ~31 GPa respectively, indicating the onset of a subtle instability. The emergence of a new Raman mode (~181 cm(-1)) at ~24 GPa and a sudden large increase in the intensity of the A1g(1) mode signify the occurrence of a symmetry lowering structural transition of the parent tetragonal phase with enhanced interlayer coupling. Two more modes appear at higher pressures (~33 GPa) at frequencies below the A1g(1) mode and are ascribed to a monoclinically distorted phase (space group P21/m). High pressure x-ray diffraction studies performed up to ~47 GPa confirm the occurrence of the structural transitions with decreasing crystal symmetry. These observations are consistent with a picture in which the structural distortion involves destabilization of the tetragonal unit cell following a gradual change in the bonding nature from layer-like (2D) to non-layer like (3D) involving the Cl-bilayers along the c direction.