The 49-year-old is said to have gifted Paradis a gold pendant bearing the message: My heart is always with you!
Depp has two children, Jack, 9, and Lily Rose, 13, with Paradis. The four are spending quality time at Depp's four million pounds home in Plan de La tour, France.
"They are having a family holiday to show the kids they are still a strong family even if those two are split or not," thesun.co.uk quoted a source as saying.
"But the fact he presented her with such a touching gift, it's almost as if they could make another go of things. Johnny wants to be with his family, he's a very family oriented man. His kids mean everything to him," the source added.
Depp and Paradis had been together for almost 14 years, before officially announcing their separation in June.
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