Short answers, pulled from the story.
Napoleon Bonaparte established the Council of State in 1799 as a judicial body to adjudicate claims against the State and assist in drafting important laws. This institution replaced the King's Council which had existed since the thirteenth century under various names like Curia regis.
Masters are recruited from among graduates of France's National Administration Academy who enter at the bottom rank called Auditeurs de deuxième class. Senior masters hold the title of Auditeurs de première class before advancing through the ranks based on seniority from their preceding rank.
The Council acts both as legal adviser to the executive branch and as supreme administrative court within one of two branches of French judiciary. It hears appeals on questions of law from lower courts and gives advisory opinions when referenced by those same courts.
The 3rd of February 1989 marked a decision regarding Alitalia corporation establishing that executive branch is responsible for voiding its own unlawful rules even if initially lawful. This ruling clarified government accountability despite the civil law country without formal rule of precedent.
Proceedings begin with statement of claim detailing factual background followed by formal investigation asking government agencies to satisfy it with detailed defense statements. Burden of proof does not lie with plaintiff since Council decides whether appellant has cause if information provided locates previously undisclosed evidence.