We present results from a study of the kinematic structure of star‐forming galaxies at redshift z∼ 3 selected in the VIMOS VLT Deep Survey (VVDS), using integral field spectroscopy of rest‐frame optical nebular emission lines, in combination with rest‐frame UV spectroscopy, ground‐based optical/near‐IR and Spitzer photometry. We also constrain the underlying stellar populations to address the evolutionary status of these galaxies. We infer the kinematic properties of four galaxies: VVDS‐20298666, VVDS‐020297772, VVDS‐20463884 and VVDS‐20335183 with redshifts z= 3.2917, 3.2878, 3.2776 and 3.7062, respectively. While VVDS‐20463884 presents an irregular velocity field with a peak in the local velocity dispersion of the galaxy shifted from the centre of the galaxy, VVDS‐20298666 has a well‐resolved gradient in velocity over a distance of ∼4.5 kpc with a peak‐to‐peak amplitude of v= 91 km s−1. We discovered that the nearby galaxy, VVDS‐020297772 (which shows traces of active galactic nucleus activity), is in fact a companion at a similar redshift with a projected separation of 12 kpc. In contrast, the velocity field of VVDS‐020335183 seems more consistent with a merger on a rotating disc. However, all of the objects have a high local velocity dispersion (σ∼ 60–70 km s−1), which gives v/σ≲ 1. It is unlikely that these galaxies are a dynamically cold rotating disc of ionized gas.