The Economist's blog, Free Exchange, has a post relating the characteristics of the French election to Arrow's Impossibility Theorem, (pdf proof) from Kenneth Arrow's 'A Difficulty in the Concept of Social Welfare,' The Journal of Political Economy, Volume 58, Issue 4 (August, 1950), pp. 328–346. This and his more comprehensive book 'Social Choice and Individual Values' won him the Nobel Prize in 1972. The theorem explains the inefficiency of voting systems with more than two candidates and more than one voter in determining the one candidate who is the social optimum. It can be shown that in some voting scenarios, the aggregate outcome can produce a result which is below the social optimum. In the case of France, François Bayrou was the clear social optimum, but in only a two round election system, the results were polarised in the first round between Ségozy and Sarkolène as Jean-Marie Le Pen called them. The United States also has a particularly inefficient selection system where geographic area and party affiliation vote on a candidate in the primaries, then geographic areas vote again for a president who is elected then by several hundred members of the Electoral College. For example, Albert Gore won the popular election but ultimately lost the election in the Electoral College. The inefficiency of voting systems can also be exacerbated or exploited as in Tom Delay's infamous Tejas redistricting of 2003.
It should be stated that a voting system based on modern information technology could easily be far superior to all of the 18th Century systems currently in use.