Since a European Court of Justice ruling in May 2014 recognising the "right to be forgotten" on the net, Google users can ask the search engine to remove results about them that are no longer relevant.
However, Google ran into trouble in France over the fact that while it removes these references from its results in searches made in Google.fr or other European extensions, it refuses to do so on Google.com and elsewhere.
"This strips away the effectiveness of this law, and varies the rights granted to persons according to the Internet user who consults the search engine, rather than the person concerned," said the data watchdog CNIL.
Google made no comment when contacted by AFP.
In June, CNIL ordered Google to respect the right to be forgotten in all search results, after receiving hundreds of complaints from individuals.
However Google refused to comply and in July appealed the decision, arguing that CNIL was not competent "to control" information accessed across the globe.
If the Internet giant continues to avoid compliance with the law, it faces a fine of up to 150,000 euros ($205,000).
Google has a history of legal woes in Europe where concerns are high over its use of private data.
In France the US giant was fined 150,000 euros in 2014 for failing to comply with CNIL privacy guidelines for personal data.