The couple - who have been in a 14-year relationship - have been the subject of several split rumours since the beginning of the year.
However, French singer Paradis denied the rumours in January, stating that they are "false".
When asked if they are still an item at the Dark Shadows UK premiere last night (May 9), Depp told The Sun: "The rumours are not true.
"They are absolutely not true. No matter what I say about this, people believe the opposite."
He added: "I can't say enough about it not being over."
Johnny Depp recently explained that he owes director Tim Burton a debt for his successful career.
Dark Shadows opens on May 11 in the UK and the US.
Watch Johnny Depp in the trailer for Dark Shadows below: