Depp, 52, supported his 16-year-old daughter Lily-Rose at a screening of her film The Dancer at the Cannes Film Festival earlier this month, visiting her for the weekend of May 6-8.
A source tells PEOPLE that Depp may have warned her about his impending split with Heard.
“I don’t think Johnny’s trip to Paris this month was a coincidence,” the source said.
Afterward, Depp headed back to London for a May 8 press conference promoting Alice Through the Looking Glass – but was delayed (and posed for some selfies) when his Eurostar train made an emergency stop in Calais due to smoke in one of the carriages.
Another source thought that Depp “was missing his usual spark” at the press conference. “He didn’t have his usual air,” the source said. “He didn’t do any one-on-one interviews, not even with a few favorite European journalists. Just the press conference.”
There was only one mention of Heard, 30, at the event, in reference to the couple’s dog-smuggling scandal.
Depp’s ex and Lily-Rose’s mother Vanessa Paradis was in Cannes the next week, seeing her daughter’s movie at the film festival. She was photographed in Los Angeles as news of Depp’s divorce broke and spotted visiting their son Jack’s school.
A source who has known both Depp and Paradis for decades says the couple, who dated for 14 years but never wed, are still close.
“They’re very close and Vanessa thinks of Johnny as the love of her life,” the insider says.
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Heard also spent time with Depp’s children, telling Marie Claire in November that she was enjoying being a stepmom.
“[It’s] an honor and the greatest, most surprising gift I have ever received in my life,” Heard told the magazine.