High resolution stimulated gain Raman spectroscopy is used to investigate the collisional parameters of pure rotational S-0(j = 0-4) lines of H-2 in pure H-2 and H-2-He mixture. Measurements are performed between 300 and 1000 K in a density regime where the lines are essentially collisionally broadened (typically 10 amagat). For the first time, these highly accurate measurements of the frequencies of pure rotational lines allow one to correct previously measured values that did not take into account the collisional frequency shift. For both collisional systems,the shifting coefficients exhibit a Linear behavior with the square root of temperature, similar to the behavior already observed in the Q branch. The broadening coefficients. bf the S-0 branch increase nonlinearly with temperature contrary to; the Q branch. For the H-2-He system, both these new S-0(j) data and previously measured Q(j) data are analyzed using a modeling of the broadening coefficients in terms of elastic and inelastic contributions. These different contributions are analyzed as ri function of temperature and of he rotational quantum number j. Preliminary quantum calculations are used to assess the validity of the model. Further calculations will be presented in paper II.