The controversy concerns Google's AdWords service, which allows advertisers to sponsor particular search terms so that, for a fee, whenever that term is searched the advertiser's link will appear next to the search results.
AXA accuses Google of selling its trade marked terms to rivals, according to a Reuters report.
Neither company has commented on the suit, but it is not the first time that Google has faced action in France over its AdWords service.
In October last year the search engine was ordered to pay damages of €70,000 by the Lower Court of Nanterre for allowing advertisers to sponsor the terms "bourse des vols" (flight market) and "bourse des voyages" (travel market), which were registered trade marks of the travel agencies Luteciel and Viaticum.
Controversially, despite the terms in question being generic, the French court found in favour of the travel companies.
Google is facing a similar action in the US, following the January filing of a suit by The American Blind and Wallpaper Factory. Again the issue will be whether an ostensibly generic term like "American blind" can be protected.
Google has, until recently, followed a policy of screening for certain clear trade marks, such as "American Blind Factory." But it abandoned its screening policy in the US and Canada last week.
These and other legal battles do not seem to be dampening the fever surrounding the company's much-anticipated flotation. According to the Wall Street Journal, Credit Suisse First Boston and Morgan Stanley will take command of the initial public offering, which is expected to be announced this week.