We investigated magnetoelastic coupling through the field-driven transition to the fully polarized magnetic state in quasi-two-dimensional [Cu(HF2)(pyz)2]BF4 by magnetoinfrared spectroscopy. This transition modifies out-of-plane ring distortion and bending vibrational modes of the pyrazine ligand. The extent of these distortions increases with the field, systematically tracking the low-temperature magnetization. These distortions weaken the antiferromagnetic spin exchange, a finding that provides important insight into magnetic transitions in other copper halides.