If you are an American, over 18 years of age, residing and working in France for over five years, you may be eligible to apply for French naturalization. Americans, along with the British and Australians, are allowed dual citizenship. You do not have to relinquish your American passport to become a French citizen, and therefore a member of the European Community.
There are no history or cultural tests; you do not even have to be able to sing La Marseillaise - just weather the French bureaucracy. The most commonly travelled roads to French citizenship are via family relations, having a French parent or spouse, and by residency - making the leap from carte de residént to citizenship. Family related applications go through your local small claims court or Tribunal d’Instance and usually take about a year to process if there are no major complications.