George and Amal Clooney are ready to defend their infant twins in court ... as they vow to sue a French magazine that published pics of them.

The mag, "Voici," published shots on Friday of the Clooneys cradling Alexander and Ella. They appeared to be in a backyard, and George says that's exactly what happened ... and he's pissed.

In a statement he says, "Over the last week photographers from Voici magazine scaled our fence, climbed our tree and illegally took pictures of our infants inside our home. Make no mistake the photographers, the agency and the magazine will be prosecuted to the full extent of the law."

Assuming it went down as George said ... he's got a strong case. Under French law, public figures -- like George -- can only be photographed while going about their public lives ... and only for journalistic purposes.

Even in Italy -- where George and Amal were in the photos -- photogs cannot peep into a private residence or take photos of people or objects hidden from normal visibility.

George says, "The safety of our children demands" he go forward with a lawsuit.

The magazine responded saying the pictures published "are a response to a public demand" and that the pictures "do not put in danger Mr. Clooney, his wife or their kids."