The order today from CNIL comes more than a year after Europe's highest court ruled that people have the right to control what appears when their name is searched online.
So far, Google says it has received more than 268,000 requests to remove URLS after the May 2014 decision, but switching to a non-European Google domain can pull up deleted links.
Isabelle Falque-Pierrotin, president of CNIL, said the order to remove search results globally "is only telling international companies that operate in Europe that they must conform to European law."