The Dark Energy Spectroscopic Instrument (DESI) is under construction to measure the expansion history of the Universe using the Baryon Acoustic Oscillation technique. The spectra of 35 million galaxies and quasars over 14000 deg² will be measured during the life of the experiment. A new prime focus corrector for the KPNO Mayall telescope will deliver light to 5000 fiber optic positioners. The fibers in turn feed ten broad-band spectrographs. A consortium of Aix-Marseille University (AMU) and CNRS laboratories (LAM, OHP and CPPM) together with LPNHE (CNRS, Universities Pierre et Marie Curie and Paris-Diderot) and the WINLIGHT Systems company based in Pertuis (France), are in charge of integrating and validating the performance requirements of the full spectrographs. This includes the cryostats, shutters and other mechanisms. The first spectrograph of the series of ten has been fully tested and the performance requirements verified for the following items: focus, image quality, straylight, stability, detector properties and throughput. We present the experimental setup, the test procedures and the results.