Records of civil registration are typically held in registries in local town halls (mairie). Copies of these registries are deposited each year with the local magistrate's court and then, when they are 100 years old, are placed in the archives for the town's Department. Due to privacy regulations, only records over 100 years old may be consulted by the public. It is possible to obtain access to the more recent records, but you will generally be required to prove, through the use of birth certificates, your direct descent from the person in question.
Birth, death, and marriage records in France are full of wonderful genealogical information, though this information varies by time period. The later records usually provide more complete information than the earlier ones. Most civil registers are written in French, though this doesn't present a great difficulty to non-French speaking researchers as the format is basically the same for most records. All you need to do is learn a few basic French words (i.e. naissance=birth) and you can read pretty much any French civil register. This French Genealogical Word List includes many of the common genealogy terms in English, along with their French equivalents.
One more bonus of French civil records, is that birth records often include what is known as "margin entries." References to other documents on an individual (name changes, court judgments, etc.) are often noted in the margins of the page containing the original birth registration. From 1897, these margin entries will also often include marriages. You'll also find divorces from 1939, deaths from 1945, and legal separations from 1958.
Births (Naissances)Births were usually registered within two or three days of a child's birth, usually by the father. These records will typically provide the place, date and time of registration; the date and place of birth; the child's surname and forenames, the parents' names (with mother's maiden name), and the names, ages, and professions of two witnesses. If the mother was single, her parents were often listed as well. Depending upon the time period and locality, the records may also provide additional details such as the age of the parents, the father's occupation, the birthplace of the parents, and the relationship of the witnesses to the child (if any).
Marriages (Mariages)After 1792, marriages had to be performed by civil authorities before couples could be married in the church. While church ceremonies were usually held in the town where the bride resided, civil registration of the marriage may have taken place elsewhere (such as the groom's place of residence). The civil marriage registers give many details, such as date and place (mairie) of the marriage, full names of the bride and groom, the names of their parents (including mother's maiden surname), the date and place of death for a deceased parent, the addresses and occupations of the bride and groom, details of any previous marriages, and the names, addresses, and occupations of at least two witnesses. There will also usually be an acknowledgement of any children born before the marriage.
Deaths (Décès)Deaths were usually registered within a day or two in the town or city where the person died. These records can be especially useful for people born and/or married after 1792, because they may be the only existing records for these individuals. The very early death records often only include the full name of the deceased and the date and place of death. Most death records will also usually include the age and birthplace of the deceased as well as the parents' names (including mother's maiden surname) and whether or not the parents are also deceased. Death records will also usually include the names, ages, occupations, and residences of two witnesses. Later death records provide the marital status of the deceased, the name of the spouse, and whether the spouse is still alive. Women are usually listed under their maiden name, so you will want to search under both their married name and their maiden name to increase your chances of locating the record.