Once arriving in France, it is required to apply for the Carte de Sejour within three months of your arrival date. The process is relatively simple. You mail the residence form given to you by the French consulate (in the US where you got your Visa), to the nearest French Office of Immigration and Integration (OFII). You'll complete the form with your address in France and include your Visa number. You'll also send them a photo copy of your passport ID page and the Visa page. It must be mailed by certified mail. The post office can help if you need clarification.
The OFII will first sent you a letter acknowledging receipt of your form and next they'll send you a letter with an appointment time and date. We received ours within a couple weeks of sending in our forms. You report to the office for your appointment with the required paperwork which they specify in the letter ( proof of address, ID photos, passport, and payment or receipt of fees paid online).
For your appointment, they begin with a medical exam which includes a chest x-ray, weight check, vision test, blood pressure check, and a few questions about immunizations and health insurance. (They did not ask for shot records or proof of insurance. They simply asked if we'd had our shots and if we had US health insurance). A doctor also listens to your heart and breathing. Then you meet with the person who will apply your Carte de Sejour (basically a sticker) inside your passport. You must either bring a money order with you or pay online- for us it was 241 Euros per person! They'll tell you how much you owe before you come. If you pay on their website before your appointment, just bring a copy of the receipt. This was the easiest option since you can simply use your credit or debit card. Fortunately children DO NOT need a Carte de Sejour since they are with you.
If you stay in France more than a year, you can report to your nearest prefecture to reapply. You don't have to return to the OFII office. You can apply for the extension within 2 months of the expiration of your Carte de Sejour. They explain all this to you when you get the Carte de Sejour at the OFII office.
Everyone at the office spoke English and they were friendly and helpful. The entire process probably took 1 hour.