The microquasar GX 339−4, known to exhibit powerful compact jets that dominate its radio to near-infrared emission, entered an outburst in 2010 for the fifth time in about 15 yr. An extensive radio to X-ray multiwavelength campaign was immediately triggered, and we report here on European Southern Observatory/FORS2+ISAAC optical and near-infrared spectroscopic observations, supported by Australia Telescope Compact Array radio and Rossi X-ray Timing Experiment/Swift X-ray quasi-simultaneous data. GX 339−4 was observed at three different epochs, once in the soft state and twice in the hard state. In the soft state, the optical and near-infrared continuum is largely consistent with the Raleigh-Jeans tail of a thermal process. As an explanation...