The observation of the Higgs boson solidified the standard model of particle physics. However, explanations of anomalies (for example, dark matter) rely on further symmetry breaking, calling for an undiscovered axial Higgs mode. The Higgs mode was also seen in magnetic, superconducting and charge density wave (CDW) systems. Uncovering the vector properties of a low-energy mode is challenging, and requires going beyond typical spectroscopic or scattering techniques. Here we discover an axial Higgs mode in the CDW system RTe₃ using the interference of quantum pathways. In RTe₃ (R = La, Gd), the electronic ordering couples bands of equal or different angular momenta. As such, the Raman scattering tensor associated with the Higgs mode contains both symmetric and antisymmetric components, which are excited via two distinct but degenerate pathways. This leads to constructive or destructive interference of these pathways, depending on the choice of the incident and Raman-scattered light polarization. The qualitative behaviour of the Raman spectra is well captured by an appropriate tight-binding model, including an axial Higgs mode. Elucidation of the antisymmetric component is direct evidence that the Higgs mode contains an axial vector representation (that is, a pseudo-angular momentum) and hints that the CDW is unconventional. Thus, we provide a means for measuring quantum properties of collective modes without resorting to extreme experimental conditions.