His relationships were long and monogamous, even if some of them were, to put it mildly, tumultuous.
His relationship with Kate Moss in the mid-Nineties was intense and passionate, but not quite as in the legends.
He denies the story about filling a bath with champagne at the Portobello Hotel in which he and Moss supposedly bathed.
"I wish it was true," he says, with a sad little smile.
He is clearly uneasy talking about Kate, whom he's not spoken to since they split up.
One feels this is more out of loyalty to Paradis than lack of love for Moss.
"I was not good for Kate," he says. "But she's a strong girl and a great girl and very smart."
He says he was shocked at her treatment by newspapers, who nicknamed her Cocaine Kate.
"Dragging her through the mud like that - they are weird and two-faced.
"Let her be! I have never met Pete Doherty, but I think he has talent and he and Kate could be great together.
"She's got a great brain on her and she's a good mummy."
Depp met Paradis, whom he touchingly refers to as "my girl" - possibly the only man in the world who could use this term of endearment without it sounding ridiculous - in France in 1998.
He was filming the Roman Polanski movie The Ninth Gate at the time.
It was one of those instant connections.
"You have this feeling - I can't really explain what it was, but I had it when I met Vanessa.
I saw her across a room and I thought: "What's happening to me?"
"I had no way of knowing how great a person she was or how great a mother she would be.
"I can remember thinking the last thing in the world I wanted was a relationship, but it was impossible to escape. I was gone."
Paradis, despite her pop star background and having a hit with Joe Le Taxi when she was 14, came from a very stable, sensible background.
She still looks like a luscious Lolita, all angular cheekbones and big eyes.