The ionic Fokker–Planck code which was written for describing plasma shock wave fronts [M. Casanovaetal. Phys. Rev. Lett.67, 2143 (1991)] is applied to model the collision of two plasmas in plane geometry. Improvements brought to the code for that purpose are described. The initial phase of the experiment during which the plasmas interpenetrate is accounted for by a simple fluid model, which yields qualitative insight into the phenomena at play as well as an initial condition to start the kinetic simulation. The kinetic results obtained in the stagnation and thermalization phases are discussed with respect to a specific laser‐produced plasma collision experiment, as well as to existing fluid and kinetic (‘‘particle‐in‐cell’’) simulations.