Briefly, about the French electoral system:
French presidential elections use a run-off system whereby, if no one candidate receives 50% or more of the vote in the first round, the top two vote getters move on to the second round. The candidate that receives 50% or more of the vote then is then elected President. The term is now five years (which changed in 2000, down from seven). The first round of voting is held on a Sunday near the end of April and the second round, if necessary, is held two weeks later. This has the effect of putting May Day (or Labor Day, May 1st), a historically important day for protests and demonstrations, in between the two rounds. This has had explosive results in the past.
On to the history:
This election, as all elections do, took place in the shadow of its predecessor, the 2002 Presidential Election. This previous election had something of a scarring effect on the French psyche as a result of the success of the extreme-right/nationalist candidate, Jean-Marie Le Pen, in the first round, earning him a place in the second round against Chirac. After founding his party, the National Front, in 1972, Le Pen ran for President in 1974, 1988, 1995, and, of course, 2002. His presence was always a thorn in the side of the French political mainstream (particularly the left) though the fact that it seemed unlikely that he would ever make it to the second round (getting about 15% of the vote in most elections) minimized the appearance of his threat. In 2002, however, the vote amongst the left was divided between upwards of 8 parties, each getting between 16.2% (Socialist Party) and less than 1% (Party of the Workers). The majority of these smaller parties received between 2% and 6% of the vote. (To see how divided the left really was, one need only to look at the names of the parties which included the French Communist Party, the Revolutionary Communist League, the aforementioned Party of the Workers, the Workers Struggle party, and, of course, the Greens.) Given this division on the left, no major center-right candidate other than Chirac, and Le Pen's historical best performance (16.8%), the result of the second round put Chirac and Le Pen together for the second round.
The majority of the political spectrum, any one left of the extreme right, was shocked and, to some degree, ashamed that such an extreme figure could make it to the highest electoral round. Esther tells me about her experience that night where, as soon as the results were announced at 8pm, you could here the demonstrations beginning in the street. She joined them and remained out until 4 or 5am when finally the gendarmes came out with tear gas and water hoses to send everyone home. (Esther informs me that tear gas hurts.) This, of course, was just the night of the election and happened without any advanced planning. On May Day over 1.3 million people across France (more than 400,000 in Paris alone) demonstrated against Le Pen and made it pretty clear that at least he wouldn't be President.
When the second round came, Chirac prevailed, receiving the largest portion of the vote (82%) in the history of the fifth French Republic. It really stuck in the craw of the leftists to have to vote for Chirac and to contribute to his third-world-like landslide victory, but given the choices, there was no other option.
So, Chirac became president and did his thing for the next five years. His opposition to the Iraq War earned him a great deal of appreciation here and abroad but really, his second term was not particularly remarkable. In retrospect, what was perhaps most notable, was the ascension of a short-in-stature but big-in-presence, "tough on crime" firebrand through various ministerial positions. Though his name wasn't particularly well-known before the 2005 riots, it is certainly well-known now: Nicolas Sarkozy.