The decree authorising the new law was published on Wednesday, and French authorities say they now have to deal with over 6,000 requests that have been made since the law was passed a month ago.
France's constitutional court in October ruled the 2004 law banning the use of the French words for such terms as xenophobia, Satan, mosque, slave, Jew, brothel, church, cannabis and business was unconstitutional.
"More than 6,100 requests have been made," since July 1, Mathieu Weill of the French Association for Internet Naming and Cooperation (AFNIC) told AFP.
Anyone who can demonstrate a "legitimate interest" and was the first to put in a request since the new law came into effect will get the domain name they want.
For sensitive names such as those of religions, an applicant can be refused because of the risk of "disturbing public order," Weill said.
The law's decree also says that offices receiving requests for domain names should tell the government immediately "of requested or registered domain names that are obviously illicit or against public order."