Weyl semimetals are 3D phases of matter with topologically protected states that have remarkable macroscopic transport behaviors. As phonon dynamics and electron-phonon scattering play a critical role in the electrical and thermal transport, we pursue a fundamental understanding of the origin of these effects in type-I Weyl semimetals NbAs and TaAs. In the temperature-dependent Raman spectra of NbAs, we reveal a previously unreported Fano lineshape, a signature stemming from the electron-phonon interaction. Additionally, the temperature dependence of the A₁ phonon linewidths in both NbAs and TaAs strongly deviate from the standard model of anharmonic decay. To capture the mechanisms responsible for the observed Fano asymmetry and the atypical phonon linewidth, we present first principles calculations of the phonon self-energy correction due to the electron-phonon interaction. Finally, we investigate the relationship between Fano lineshape, electron-phonon coupling, and locations of the Weyl points in these materials. Through this study of the phonon dynamics and electron-phonon interaction in these Weyl semimetals, we consider specific microscopic pathways which contribute to the nature of their macroscopic transport.