We present VLT spectroscopic observations of 7 discovered galaxy groups between 0.3<z<0.7. The groups were selected from the Strong Lensing Legacy Survey (SL2S), a survey that consists in a systematic search for strong lensing systems in the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS). We give details about the target selection, spectroscopic observations and data reduction for the first release of confirmed SL2S groups. The dynamical analysis of the systems reveals that they are gravitationally bound structures, with at least 4 confirmed members and velocity dispersions between 300 and 800 km/s. Their virial masses are between 10^13 and 10^14 M_sun, and so can be classified as groups or low mass clusters. Most of the systems are isolated groups, except two of them that show evidence of an ongoing merger of two sub-structures. We find a good agreement between the velocity dispersions estimated from the analysis of the kinematics of group galaxies and the weak lensing measurements, and conclude that the dynamics of baryonic matter is a good tracer of the total mass content in galaxy groups.