So what does the President of France do anyway?Mike Rappaport

This Wikipedia entry is useful, although I am not really in a position to judge its accuracy.  The French system is interesting.  More like the constitutional structure of the United States than many would have thought.  In many ways, it actually resembles the 18th century British system, which the Framers copied and which was developing into a parliamentary system, but was not there yet.  The President is the King, but he must govern through Parliament.  In Israel, by contrast, the President is the King, but a king who merely reigns and dose not rule. 

Here is an excerpt on the President’s powers:

In the original 1958 constitution, the President was electedby an electoral college of elected officials. However,in 1962, Charles de Gaulle obtained, through a referendum,an amendment to the constitution whereby the president would be directlyelected by citizens.[7]Given France’s runoff voting system,[8]this means that the presidential candidate is required to obtain a nationwidemajority of non-blank votes at either the first or second round of balloting,which presumably implies that the president is somewhat supported by at leasthalf of the voting population; this gives him considerable legitimacy. Despitehis somewhat restricted de jure powers, the president thus enjoys considerable auraand effective power.

As a consequence, the President is the preeminent figure inFrench politics. He appoints the Prime Minister;[9]though he may not de jure dismiss him, if the Prime Minister is from the samepolitical side, he can, in practice, have him resign on demand (and it is knownthat Prime Ministers are asked to sign a non-dated dismissal letter beforebeing nominated). He appoints the ministers, ministers-delegate andsecretaries. When the President’s political party or supporters controlparliament, the President is the dominant player in executive action, choosingwhomever he wishes for the government, and having it follow his politicalagenda (parliamentary disagreements do occur, though, even within the sameparty).

However, when the President’s political opponents controlparliament, the President’s dominance can be severely limited, as he mustchoose a Prime Minister and cabinet who reflect the majority in parliament, andwho will implement the agenda of the parliamentary majority. When parties fromopposite ends of the political spectrum control parliament and the presidency,the power-sharing arrangement is known as cohabitation. Cohabitation used to happenfrom time to time before 2002, because the mandate of the President was 7 yearsand the mandate of the Assemblée Nationale was 5 years. Now that the mandate ofthe President has been shortened to 5 years, and that the elections are separatedby only a few months, this is less likely to happen.

And what entry would be complete without some reference to their system of constitutional review:

Neither the judiciary nor the administrative courts can ruleupon the constitutionality of statutorylaw. While technically not part of the judiciary, the ConstitutionalCouncil examines legislation and decides whether it conforms to the constitutionand treaties,prior to its promulgation: in all cases for organic laws, and only underreferral from the President of the Republic, the president of the Senate, thePresident of the National Assembly, the PrimeMinister or 60 senators or 60 members of the NationalAssembly for normal laws. The Constitutional Council may refuse statutes asunconstitutional if they contradict the principles of the 1789 Declaration of theRights of Man and of the Citizen (cited in the preamble of theConstitution) or the European Convention on Human Rights(accepted by treaty).  The Constitutional Council comprises members appointed for 9years (3 every 3 years), three members appointed by the President, threemembers appointed by the President of the National Assembly, and threeappointed by the President of the Senate.