"Make no mistake, Johnny is not walking away from his kids, at all," insists the insider. "He loves his children, more than life itself, and he is determined to remain a constant everyday presence in their lives."
And while we hold out hope for a Depp-Winona Ryder reunion (complete with the reinstatement of his "Winona Forever" tattoo, which was changed to "Wino Forever" after their split), he's keeping busy with the big-budget "Lone Ranger" flick, which is shooting in New Mexico and Colorado through the summer.
As for Paradis, she surfaced last week at a film festival in Paris, but she apparently didn't much feel like flashing her fetchingly gap-toothed smile.
"She looked tired," says a People source. "She just didn't look well or happy."