We report the first direct measurement of near-band-gap Franz-Keldysh electrorefraction in Al0.3Ga0.7As/GaAs/Al 0.3Ga0.7As p-i-n single-crystal thin-film Fabry-Perot structures with semitransparent metallic mirror contacts. These measurements are performed for various reverse biases and at photon energies ranging from 9 to less than 1 meV from the GaAs band edge. The measured refractive index variation is several times larger than that predicted by the effective mass approximation theory.