The Pirates of the Caribbean star began dating French singer Paradis in 1998 and they set up home in the south of France with their two children, Lily-Rose, 12, and Jack, nine.
But a new People magazine article suggests Depp’s huge success has caused tension in the relationship amid speculation the couple is now leading separate lives.
A source tells the publication, “Vanessa went seven years between albums, and several years between film projects, while he became Captain Jack Sparrow (from Pirates of the Caribbean).”
The rumours are further fuelled by allegations Paradis intentionally skipped the Paris premiere of Depp’s The Rum Diary last November (11).
The insider says, “She went instead to a concert that night. It was weird and pretty clear: you’re in town and don’t go to the premiere of your husband’s (sic) film? One which he starred in, (and) produced?”
A representative for Depp had yet to respond to requests for a comment as WENN went to press.
The couple last walked a red carpet together at the Cannes Film Festival in 2010.