The local nuclear and electronic structures and molecular dynamics of the ferroelectric lattice in selected geometric fluorides (BaMgF4, BaZnF4, BaMg1-xMnxF4 and BaMg1-xNixF4; x = 0.001 and 0.005) have been investigated. The F-19 and Mg-25 isotropic chemical shift delta(iso), Mg-25 quadrupolar coupling constants (C-q) and asymmetry parameters (eta) reflect the geometry of the coordination spheres. The zero-field splitting parameters vertical bar D vertical bar and vertical bar E vertical bar are consistent with distorted axial symmetry (low temperatures) and nearly rhombic symmetry (high temperatures) of octahedral Mn2+ coordination. The high resolution of the nuclear magnetic resonance, electron paramagnetic resonance and phonon spectra are consistent with the highly ordered crystallographic structure. Combined multi-technique data evidence the subtle discontinuous changes in the temperature dependences of vertical bar D vertical bar and vertical bar E vertical bar, isotropic chemical shifts delta(iso) and signature parameters of Raman bands and suggest a discontinuous structural distortion of the fluoride octahedra. The temperature at which this change occurs depends on the ionic radius of the central ion of the octahedral site and is estimated to be similar to 300 K for Zn2+ fluorides and similar to 240 K for Mg2+ fluorides. This geometrical distortion modifies the lattice dynamics and originates from the rotation of the fluoride octahedra around a new direction approximately perpendicular to that related to the paraelectric-ferroelectric phase transition.