An injunction, if granted, would lead to the magazine being withdrawn from shelves immediately.
The royal couple will seek to have French magazine Closer withdrawn from sale after it printed the images.
The photographs have also appeared on several foreign websites and in the Irish Daily Star.
The lawyers will also ask French prosecutors to bring criminal charges against the photographer responsible.
An injunction, if granted, would lead to the magazine being withdrawn from shelves immediately but the tribunal's judgement will only relate to the distribution of the photos in France.
The action would not stop Closer's Italian sister magazine, Chi, from publishing the same photos but the speed with which the royal couple have acted may deter others from publishing the pictures.
Chi has said it plans to print a 26-page special featuring the photographs.
Closer and Chi are both part of former Italian Prime Minister Silvio Berlusconi's Mondadori media group.
Our correspondent says this is only the first step in the legal battle - St James' Palace said that alongside a civil case against the magazine they would be making a criminal complaint against the as-yet-unnamed photographer who took the pictures.
Under French law the damages could run into tens of thousands of euros and in theory the magazine editor could be sent to jail for a year.
She has already defended publication, insisting the photos were not the least bit shocking, and has suggested that she has more intimate photos not yet published.
The co-owners of the Irish Daily Star - Northern and Shell and Independent News and Media - condemned the decision to publish the pictures and said they had had no prior knowledge of it.
No British newspaper has printed the pictures, with the Daily Mail saying it had been offered similar pictures last week but had rejected them and the Sun saying that no responsible newspaper "would touch them with a bargepole".
A palace spokeswoman said: "We can confirm that a criminal complaint is to be made to the French Prosecution Department.
"It concerns the taking of photographs of the Duke and Duchess of Cambridge whilst on holiday and the publication of those photographs in breach of their privacy."
The photographs were taken while the duchess was sunbathing on a private holiday with her husband at the French chateau of the Queen's nephew, Lord Linley, in Provence.
Meanwhile, the royal couple have been in the Solomon Islands representing the Queen on their nine-day Diamond Jubilee tour of South East Asia and the South Pacific.
Prince William and Catherine were welcomed with traditional garlands when they arrived on Sunday.
Thousands of islanders cheered the couple as they travelled through the streets of the capital Honiara in a truck decorated as canoe.
The duke and duchess wore traditional dress at the home of Governor General Frank Kabui and posed for photographs at a state dinner where William tried the local dialect to thank the islands for being a place of such tranquility.
Earlier, they attended a service of thanksgiving for the Diamond Jubilee of the Queen who is the Solomon Islands' head of state.