Just as a footnote to add to all the other very good answers to this question, there are also several factors that allow French unions to punch way above their 10% weight. They are concentrated among government workers, and include many professions where their equivalents would be forbidden to strike in the US precisely because the impact of a strike is considered to great to bear, like air traffic control. Secondly, they can strike for political issues. Many issues that would be company-specific in the US, like pensions or health benefits, are structured in France so as to be transparently political and to include the whole nation. Thirdly, France is centralized in such a way that Paris is like New York, Washington and Los Angeles rolled into one; paralyze that and you've paralyzed the nation. And lastly, to build on what Doug said, the willingness of the French people to see disruptive action as legitimate, and to sympathize or feel themselves represented by it, is amazing to outsiders. During the 1996 mass strikes, there were millions of people who took 3 to 6 hours to commute to work every day, and yet they continued by a large majority to support the strike for a month and a half. And this in an era when left ideology seems almost spent by comparison with the past.
Michael