We demonstrate the spectral upconversion of a unipolar subpicosecond terahertz (THz) pulse, where the THz pulse is the Coulomb field of a single relativistic electron bunch. The upconversion to the optical allows remotely located detection of long wavelength and nonpropagating components of the THz spectrum, as required for ultrafast electron bunch diagnostics. The upconversion of quasimonochromatic THz radiation has also been demonstrated, allowing the observation of distinct sum- and difference-frequency mixing components in the spectrum. Polarization dependence of first and second order sidebands at ωopt±ωTHz, and ωopt±2ωTHz, respectively, confirms the χ(2) frequency mixing mechanism.