The official said both sides knew all along that the tree would go later into quarantine. On Monday, Trump and Macron posed for photos while planting the tree in front of the White House.
In fact, the tree, from Belleau Wood in France where nearly 2,000 American soldiers died in a World War One battle, had been dug up not long after it was planted.
Any plants and seeds brought into the USA must be tested before being allowed on American soil.
"It will soon be replanted in the White House gardens", the source said.
The official reportedly said the tree is doing well.
The planting of the tree was one of many moments from the three-day visit. Last year, when Trump announced that he was withdrawing from the accord, Macron posted an online video urging viewers to "make our planet great again" and inviting climate scientists to move to France.
5 storylines for Sunday's race in Azerbaijan
Canadian Lance Stroll, third in Baku a year ago , will start 10th for Williams - the only team yet to score a point this season. There was early drama when the Toro Rosso cars of Frenchman Pierre Gasly and New Zealander Brendon Hartley almost collided.
But after a state visit to the USA this week, he admitted he had failed to secure any promise from Trump to keep the deal alive.
Downing Street said May, Merkel and Macron also pledged to "continue working closely" with the USA on the issue, including on "those issues that a new deal might cover".
"The friendship between our two nations - and ourselves, I might add - is unbreakable".
US National Security Advisor John Bolton said Sunday that Trump had not yet decided whether or not to scrap the pact.
European leaders reaffirmed their commitment to protect the region's trade interests and address elements of a nuclear accord with Iran, even as attempts to lobby the USA president on those issues last week appeared to have failed.