The Fröhlich coupling strength of individual GaAs nanowires is investigated by resonant micro-Raman spectroscopy measurements near the direct bandgap E[subscript g]2. Large 2LO/1LO intensities up to 5.7 are observed in an individual GaAs nanowire. A 2LO resonance profile of the GaAs nanowire agrees well with a two-phonon-scattering model, suggesting excitonic scattering. These results advance the understanding of electron-phonon coupling and exciton scattering in quasi-one-dimensional systems and in GaAs at E[subscript g], allowing for the development and optimization of nanowire optoelectronic devices.