Due to their large distances, high‐redshift galaxies are observed at a very low spatial resolution. In order to disentangle the evolution of galaxy kinematics from low‐resolution effects, we have used Fabry–Pérot 3D Hα data cubes of 153 nearby isolated galaxies selected from the Gassendi Hα survey of SPirals (GHASP) to simulate data cubes of galaxies at redshift z= 1.7 using a pixel size of 0.125 arcsec and a 0.5 arcsec seeing. We have derived Hα flux, velocity and velocity dispersion maps. From these data, we show that the inner velocity gradient is lowered and is responsible for a peak in the velocity dispersion map. This signature in the velocity dispersion map can be used to make a kinematical classification, but misses 30 per cent of the regular rotating discs in our sample. Toy models of rotating discs have been built to recover the kinematical parameters and the rotation curves from low‐resolution data. The poor resolution makes the kinematical inclination uncertain and the position of galaxy centre difficult to recover. The position angle of the major axis is retrieved with an accuracy higher than 5° for 70 per cent of the sample. Toy models also enable us to retrieve statistically the maximum velocity and the mean velocity dispersion of galaxies with a satisfying accuracy. This validates the use of the Tully–Fisher relation for high‐redshift galaxies, but the loss of resolution induces a lower slope of the relation despite the beam smearing corrections. We conclude that the main kinematic parameters are better constrained for galaxies with an optical radius at least as large as three times the seeing. The simulated data have been compared to actual high‐redshift galaxy data observed with VLT/SINFONI, Keck/OSIRIS and VLT/GIRAFFE in the redshift range 3 > z > 0.4, allowing us to follow galaxy evolution from 11 to 4 Gyr. For rotation‐dominated galaxies, we find that the use of the velocity dispersion central peak as a signature of rotating discs may misclassify slow and solid body rotators. This is the case for ∼30 per cent of our sample. We show that the projected local data cannot reproduce the high velocity dispersion observed in high‐redshift galaxies except when no beam smearing correction is applied. This unambiguously means that, unlike local evolved galaxies, there exists at high redshift at least a population of disc galaxies for which a large fraction of the dynamical support is due to random motions. We should nevertheless ensure that these features are not due to important selection biases before concluding that the formation of an unstable and transient gaseous disc is a general galaxy formation process.
