The conflict stems from Google's autocomplete feature that suggests what search people might want based on algorithms of previous searches.
Because users of Google.fr frequently ask whether politicians, actors or other celebrities are Jewish or not, the word "Jew" in French is frequently suggested as what those using the search engine might in fact be asking about.
SOS Racisme, the Movement against Racism and for Friendship between Peoples (MRAP) and the International League Against Racism and anti-Semitism (LICRA) argue that Google is unintentionally breaking the law.
Google users "are confronted daily by the unsolicited and almost systematic association of the word 'Jew' with the names of the best-known people in the world of politics, the media or business," the groups say.
Under French law, it is illegal to record someone's ethnicity in a database.
Judge Martine Provost-Lopin accepted a request from all parties to appoint a mediator to find a solution, with a next hearing set for June 27, said SOS Racisme's lawyer Patrick Klugman.
"We will discuss more philosophy than law, more technical solutions than who is right or wrong," Klugman said, adding that the mediator was former business court judge Jean-Pierre Mattei.
A Google France spokesman told AFP on Tuesday that autocomplete results were "generated completely automatically, based purely on algorithmic criteria that correspond notably with the popularity of web users' inputs."
"Google does not decide on these requests in a manual way – all requests shown by autocomplete have previously been searched for by users on Google," the spokesman said, asking not to be named.