The FrenchAcademy is an official institution of 40 members that study and observe the French Language. Their dictionary is a reflection of the FrenchStandardLanguage but it's generally criticised as well as respected.

The official task is to sanction the best usage of the French language. See FrenchUsage. They also provided a grammar, but this work was extremely heavily criticised, and never reached to impose a real standard on that front.

-- PieterJansegers

''Does the French Academy have authority over public signs and airwaves in France?  I've heard that in France, you're not allowed to publish articles that, for example, say "byte" when they could say "octet".''

No, the Academy only has a moral authority. But the French Parlament voted a law in this sense. Even websites in France are now using the French "courriel" and not longer "email".
Webmaster becomes webmestre, and so on. Only the people in the street don't follow that example while speaking ! Realism is sometimes for away... :-)