.fr is the top-level-domain for France, the country of wine, chansons and good food - and moreover, one of the biggest and most influential countries of Europe. An import business partner for most European countries, therefore. That makes .fr a great domain for companies that want to aim at this giant market, and a great extension for Francophiles.
Despite the size of the country, France has a rather low online participation. This is partly due to the fact that .fr became free for registration quite late. Since the register AFNIC made it available, the amount of registered .fr domains increased quickly. In 2009 1,5 million .fr domain were registered. On a population of 60 million this is still not that much, so there are more than enough chances to register the domain that you want.
.fr is managed by AFNIC. This company also manages the extensions .tf, for the French Southern and Antarctic Lands, .re for Re`union and .wf for Wallis and Futuna Islands, wich are all overseas territories of France.
Registration of a .fr domain is restricted to companies within France, foreign companies that are active in France and residents of France. It is possible to register a .fr domain at second-level, but also on third-level, for example under .com.fr or .gouv.fr.
If a certain domain already exists at third-level, for example domat.com.fr, then the owner has the exclusive right to register the second-level-domain, wich would be domat.fr.