Any competent cavalry commander of any nation would not commit his entire force into a charge. The cavalry of all nations actually operated tactically by squadrons, not regiments, so a typical French brigade would comprise 6 or 8 squadrons. At least one third of these ought to be held back in reserve (really good tactical practice would have been to have them in three waves) and the brigade commander should be with the reserves, so that he can decide whether to commit these to reinforce success or whether they are needed to recover the leading squadrons from a disaster. In such a circumstance the leading squadrons in the charge would be led by one of the regimental commanders.
Of course if a cavalry division was committed then it would be entirely likely that the entire first brigade would charge, with the second forming the reserve. In such a circumstance the brigade commander may well lead the charge.