Raman scattering in the three-dimensional Dirac semimetal Cd3As2 shows an intricate interplay of electronic and phonon degrees of freedom. We observe resonant phonon scattering due to interband transitions, an anomalous anharmonicity of phonon frequency and intensity, as well as quasielastic (E~0) electronic scattering. The latter two effects are governed by a characteristic temperature scale T* ~ 100 K that is related to mutual fluctuations of lattice and electronic degrees of freedom. A refined analysis shows that this characteristic temperature corresponds to the energy of optical phonons which couple to interband transitions in the Dirac states of Cd3As2. As electron-phonon coupling in a topological semimetal is primarily related to phonons with finite momenta, the back action on the optical phonons in only observed as anharmonicities via multi-phonon processes involving a broad range of momenta. The resulting energy density fluctuations of the coupled system have previously only been observed in low dimensional or frustrated spin systems with suppressed long range ordering.