Yes, of course; I meant that the PM functions as a CoS only when Pres and Chambre are controlled by the same "famille politique" - eg, Villepin, Raffarin, Juppe, Bere, Cresson and so forth.  The comparison comes to mind because both PM and CoS (when President's coalition controls the Chmbre) really have a constituency of one, the PResidnt. And that in the American system the CoS has most direct relations with the cabinet and legislature.

In the case of a cohabitation, the PM is I think most analogous to the Speaker in an American "cohabitation" (eg, O'Neil/ Reagan; Gingrich/ Clinton).