The preliminary criminal probe, which follows a complaint lodged by the royal couple on Monday, was announced just hours before a French court was to rule on whether to ban the resale of the photos first published by Closer.
It will allow the prosecutor to decide whether to proceed with a full investigation of allegations that the taking of and publication of the
pictures breached the couple's right to privacy under French law.
The prosecutor will also have to decide who any criminal proceedings are directed against.
The royals' suit cites persons unknown but aides say they want proceedings against both the editor of Closer and the photographer or photographers who took the shots of the couple at a southern French chateau earlier this month.
The court decision was expected at 1000 GMT on the request for an injunction banning republication or resale of the photos published Friday by Closer, which is owned by Italian ex-prime minister Silvio Berlusconi's Mondadori group.
The couple's lawyer Aurelien Hamelle on Monday told the court in the Paris suburb Nanterre that the images were from "a highly intimate moment during a
scene of married life and have no place on the cover of a magazine".
Hamelle drew a parallel with the "fatal hunt" by paparazzi that led to the death of William's mother Princess Diana in a car crash in Paris in 1997.
He said they were not however requesting the withdrawal of current issues of Closer from news stands, saying "the damage is done".
No newspaper or magazine in Britain has announced plans to publish the offending photographs.
But the possibility of legal action failed to intimidate Irish and Italian titles, with the pics of Catherine sunning herself in bikini bottoms appearing Saturday in a Dublin tabloid and in Italy's Chi magazine on Monday.
Chi editor Alfonso Signorini argued the pictures represented "extraordinary reportage" and said that "for the first time, the future queen of England was appearing in a natural way, without the constraints of etiquette."
In 2006, the magazine sparked outrage in Britain when it printed a photo of a fatally injured Diana being given oxygen at the scene of the high-speed crash in a Paris road tunnel in 1997, together with details from her autopsy.
Unlike Mondadori, the media groups that jointly own the Irish paper condemned its decision to run the pictures.
Michael O'Kane, editor of the Irish Daily Star, was suspended Monday as the paper's joint owners, British group Northern and Shell and Ireland-based
Independent News and Media criticised the decision to print the snaps.
Northern and Shell said it was now taking "immediate steps" to shut down the joint venture. It remained unclear Tuesday whether Independent News would
seek to keep the paper going.
Last month, photos emerged of William's brother Prince Harry cavorting naked with women at a Las Vegas party. The two images of Harry are widely
available on the Internet but in Britain only The Sun newspaper published them.
William, the second-in-line to the British throne, and Catherine meanwhile continued their nine-day southeast Asian and Pacific tour marking Queen Elizabeth's 60 years on the throne.
They seemed at ease in the company of the topless women they were introduced to on Monday in the Solomons, where bare breasts are a normal part of public life.