The Duke and Duchess of Cambridge have won an injunction in a French court preventing the celebrity magazine Closer from publishing further paparazzi shots of the duchess sunbathing topless.

Mondadori France, Closer's publishing company, will be fined €10,000 (£8,000) a day if it publishes any more photographs or transmits them to any third party via email or any other means following Tuesday's judgment.

Mondadori, owned by the former Italian prime minister Silvio Berlusconi, will also have to pay €2,000 towards legal fees as part of the ruling following a civil action.

A court in Nanterre, near Paris, opened a separate criminal investigation on Tuesday into charges that Closer and a photographer breached the privacy of Prince William and Catherine by publishing the topless photos.

The initial investigation will be carried out by the BRDP, a branch of the French police responsible for dealing with attacks on individuals, which notably handled an investigation into a writer's sexual assault allegations against the former head of the IMF Dominique Strauss-Kahn.

If found guilty, the magazine could be fined up to €45,000 and the editor could be jailed for up to a year.

On Tuesday, in a four-page document following the civil action, judges described the pictures as a "brutal display" and required them to be handed over within the next 24 hours.

"These snapshots which showed the intimacy of a couple, partially naked on the terrace of a private home, surrounded by a park several hundred metres from a public road, and being able to legitimately assume that they are protected from passersby, are by nature particularly intrusive," the ruling decreed.

"[They] were thus subjected to this brutal display the moment the cover appeared."

The duke and duchess were thousands of miles away in the Pacific country of Tuvalu when the ruling was issued. St James's Palace was making no immediate comment.

A source said of the couple: "They welcome the injunction that's been granted. They always believed the law was broken and that they were entitled to their privacy."

In granting the injunction, the French judges sided with the royal couple, whose lawyer told the court on Monday that the photos portrayed the "profoundly intimate life of the couple" and asked: "In what name did this magazine publish these shocking photos … It was certainly not in the name of information. This has no place on the cover of a magazine or even in an article in a magazine."

Their lawyer had argued in court that the photographs were a breach of the French privacy laws and "a shocking breach of their personal intimacy".

The legal action, while not the first taken by a member of the royal family against a newspaper or magazine, was seen as a bid to put down a marker and prevent any further invasion of the duchess's privacy.

But one senior executive at a British celebrity magazine said: "I think the action has been taken while the horse is already halfway round the field."

On Saturday a second publication, the Irish Daily Star, published the photos, leading to the editor being suspended on Monday night pending the outcome of an internal investigation.

And on Monday, an Italian celebrity magazine, Chi, rushed out a special edition with 26 pages devoted to the candid photos of the future Queen.

When Closer published the photos on Friday, St James's Palace roundly condemned the move as a "grotesque" invasion of the duke and duchess's privacy "reminiscent of the worst excesses of the press and paparazzi during the life of Diana, Princess of Wales".

Closer's editor, Laurence Pieau, defended the decision to print the photos and said she did not think the photos were shocking or degrading.

She said she thought the reaction had been disproportionate and that all they had tried to do was show a young couple in love.

The pictures were taken while the duke and duchess were staying in Provence at a chateau owned by Lord Linley, the Queen's nephew.

The couple, who are currently visiting parts of south-east Asia and the Pacific for a diamond jubilee tour, were told about the pictures just ahead of a stop at a mosque in Kuala Lumpur, Malaysia.

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