bi: the exact French word is "gouvernement" and describes exactly what I said in my previous post (i.e. the executive office designated by the President, and nothing more).
Other funny factoïds:
since he's the head of the "gouvernment", our "Premier Ministre" is not elected (unlike the one in the UK).
a "cabinet" refers in France to the specific office of a given "ministre". So you can say "le cabinet du ministre de la Culture", which is only a tiny part of the "gouvernement".