We retrieve the complex optical index of single-walled carbon nanotube (CNT) films in the 0.6-800 μm spectral range. Results are obtained from a complete set of optical measurements, reflection and transmission, of free-standing CNT films using time domain spectroscopy in the terahertz (THz) and Fourier transform infrared (IR) spectroscopy in the visible-IR. Based on a Drude-Lorentz model, our results reveal a global metallic behavior of the films in the IR, and confirm their high optical index in the THz range.