Johnny Depp and Vanessa Paradis, in 2008
06/19/2012 at 04:00 PM EDT
and his longtime partner Vanessa Paradis didn't take their separation
lightly and tried valiantly to keep their family together, a source tells PEOPLE.
"They've tried for months to save the relationship," the source close to the couple says, "but have known for weeks that it couldn't be saved."
Last week, Paradis arrived in France where she is promoting her film Je Me Suis Fait Tout Petit
at the Cabourg Festival of Romantic Cinema.
The source says the timing of the couple's separation announcement purposefully coincided with Paradis's trip to France. "It was all decided before she got on that plane."
As PEOPLE reported
in January, Depp, 49, and Paradis, 39, have been living separate lives for many months.
The couple are parents to two kids
, Lily-Rose, 13, and Jack, 9.