JD-EE
In French terms I am not sure what rights, if any, a person has. But if BEA does not have a right to lay into Le Figaro for irresponsible reporting something is, IMAO, terribly terribly broken.
IMHO, the BEA didn't exactly told Le Figaro to
"shut the (whatever) up" ; their phrasing was very carefully chosen : "The BEA [...] alone has the right to communicate on the progress of the investigation. [...] any information [...] from another source is null [...]" (check the BEA site for the full sentence) : translation : "neither Airbus nor Air France nor anybody else
in the industry is supposed to communicate on this subject". Thus they don't order Le Figaro to stop publishing, they just question the reliability of Le Figaro's source, according to the fact there has been no official info from BEA.
At the end of the day, the net effect is the same : BEA 1 - Le Figaro 0.