A French person and a foreigner or two French people can get married abroad, either with French authorities or with local authorities.
If the future spouses want to get married through the French authorities, they must get informed at the French embassy or consulate (that are not always able to celebrate weddings). Requested documents may vary depending on the country, but they are generally the same as for a marriage in France. The embassy or the consulate generally takes care of displaying the banns of marriage and auditioning the future spouses.
If the marriage is celebrated by the Local Civil Registrar, the French future spouse usually has to request a certificate of marriage capacity at the French embassy or consulate. For more information, go to service-public.fr (in French only).
For the marriage to be effective in France and for it to allow the foreign spouse to come live in France, the spouses must get a transcript. The transcript comes with a French marriage certificate and a family book. A transcript request can be made at the French consulate of the country.