Theige kind of hinted at this, but Pétains inclusion seems to have been one of broadening the base of the government. Reynaud also brought in de Gaulle to give it some young military oomph. What then transpired was that Reynad and de Gaulle fx were in favour of fighting on from the colonies - or even go along with the rather outrageous scheme of a Anglo-French union (de Gaulle brought the proposal from London to Reynaud, who seemed game). At the same time Pétain was for seeking terms from the Germans, and he was in contact with the CiC Weygand - and it was Weygand who ended up darkly hinting at every damn cabinet meeting, that if Reynaud didn't seek terms from the Germans, then quite possibley Weygand could take the army and remove the government in a coup d'état. The point of this being that the French army shouldn't be forced to surrender to the Germans, but the politicians. After a while of this rubbish, Reynaud threw in the towel and stepped down, Pétain stepped up, requested terms from the Germans as per Weygand's wishes, and de Gaulle went off to London to fight on.