The difference is -- and this is characteristic of the post-1971 "Presidentialized" Fifth REpublic -- that President also has his own "cabinet" with its own "directeur" and comm. operation and policy appartus.

And of course, the PM is still an office constitutionally defined as the "head of the government" meaning the PM should be setting policy and not just implementing. In effect, this happens only during a "co-habitation" or in moments of disfunction within the governing party or coalition (which have been frequent, especially since 2002).

This leads me to the other half of the question, not raised in the post. It was widely reported over the weekend that Hollande would introduce a motion of censure against the government as a way to force Sarko and the UMP deputies to tie themselves to Villepin. But now I wonder if they will instead let him hang -- simply vote for Hollande's motion, which would effectively dissolve the government (though not the Chambre).

From Chirac's pointof view, this weould be ideal -- it would free his hand to replace Villepin while allowing (as bizarre as this sounds) allowing Villepin to save face in so far as he would not be fired and could claim  to be what everyone in French politics wants to be these days -- the victim of a "complot."