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We investigate the behavior of the Higgs (amplitude) mode whensuperconductivity emerges on a preexisting charge-density-wave state. We showthat the weak overdamped square-root singularity of the amplitude fluctuationsin a standard BCS superconductor is converted in a sharp, undamped power-lawdivergence in the coexisting state, reminiscent of the Higgs behavior inLorentz-invariant theories. This effect reflects in a strong superconductingresonance in the Raman spectra, both for an electronic and a phononic mechanismleading to the Raman visibility of the Higgs. In the latter case, our resultsare relevant to the interpretation of the Raman spectra measured experimentallyin NbSe2.

Nature and Raman signatures of the Higgs amplitude mode in the coexisting superconducting and charge-density-wave state