Context: Stark broadening of the 447.1 line of neutral helium in a weakly coupled plasma has been studied. This spectral line has a very close forbidden component. This means it is very sensitive to the plasma electron density, which is similar to hydrogen lines, for which the Stark effect is linear. Aims: The aim of this work is to supply information to be used in the spectroscopic diagnostics of plasmas. Methods: We used computer simulations in the frame of a physical model for a plasma with weak coupling between charges. The calculation includes the so-called ``ion dynamics effects'' in a natural way. The electron density, the ionic and electronic temperatures, and the perturber mass were the parameters in the calculations. Results: Simulation results relate the line width, shift, shape, and especially the ratio of intensities between the allowed and forbidden components, with the plasma parameters. These results are supplied as tables of line shapes. Tables 2-11 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/503/293