FURIOUS VANESSA PARADIS has slapped JOHNNY DEPP with a stinging ultimatum demanding that he keep his alleged lover away from their children, sources say.

The “Pirates of the Ca­ribbean” star is reportedly romancing leggy blonde Am­ber Heard, and Vanessa has vowed to protect her children – Lily-Rose, 13, and Jack, 10 – from the heartache of seeing their father in her arms, ac­cording to the sources.

Vanessa, 39, was devastated by news of her longtime love’s relationship with the bisexual beauty, and the French singer-turned-actress is preparing to wage a full-scale palimony battle for her share of his $350 million fortune, the sources add.

“Vanessa might be putting on a brave face in public, but she’s absolutely distraught,” revealed a pal. “There’s no amount of money that can take away her agony as the full picture of what actually went down with Amber slow­ly emerges.”

Johnny, 49, and Amber, 26, reportedly became close while filming “The Rum Di­ary” in 2009. But at the time, there was more speculation about him and Angelina Jolie, his co-star in the 2010 romantic thriller “The Tourist.”

But when “The Rum Diary” promo tour kicked into high gear late last year, whispers of a Johnny-Amber affair be­gan circulating, and Vanessa exploded when he draped his arm around Amber at the film’s London premiere, sources say.

“Vanessa and Johnny made a pact years ago that he would never be pho­tographed with another woman in a compromising situation, no matter how in­nocent,” explained a source.

“When he did that in Lon­don, Vanessa knew there was no going back. What she can’t believe is that Amber was most likely in the picture as far back as 2009.

“Right now, she’s angry and humiliated and not seeing things straight, but everyone believes her when she says she’ll never forgive Johnny for walking out on his family.”

As The ENQUIRER recent­ly revealed, Vanessa believes she’s due a big chunk of John­ny’s assets because they were together when he cashed in with the “Pi­rates” blockbusters.

But for now she’s fo­cused on making sure Amber doesn’t spend any time with her kids, said the pal. In fact, The ENQUIRER has learned Vanessa sent a message to Amber via their management teams that she’s to stay away from the children.

“Vanessa doesn’t want Amber anywhere near them,” confided the pal. “Obviously, she’s told Johnny her wishes, but rumors are flying that Johnny’s so obsessed with Amber that she gets away with murder. He’s even fired two of his assistants in the past four months for not keep­ing up with her demands.

“When it comes to his rela­tionship with Amber, Johnny doesn’t care who he hurts – least of all Vanessa.”