To get the full details on what you will have to do to get married in France, go to the mairie of the town in which your fiancé is resident. You have to get married at the mairie of the town of residence of one of the couple. Precise requirements vary a bit from town to town - and make sure you ask for the list of requirements for a foreigner.
It's a bit of a paper chase - some documents have to be obtained from your consulate, and others (like your birth certificate) have to be translated by a special expert translator (who also verifies the validity of the documents being translated).
The US consulate puts out a nice little report on the general requirements for a foreigner to marry a French person in France: http://photos.state.gov/libraries/france/5/acs/paris-marriage.pdf
Consult your own consulate for details about which documents are obtainable through the consulate.
The other issue is your visa status. If you're on a long-term visa, you should be able to change your carte de séjour with little or no problem. If you're on any other sort of visa, they may make you go back to your home country to apply for a spouse visa.