A French hospital plane was expected in Beirut later in the day to fly Edith Bouvier and William Daniels home but the diplomatic source said:
"Doctors will first have to carry out the necessary tests to see if they are up to the journey.
"They are both under observation in Beirut's Hotel-Dieu de France hospital," the source said.
Bouvier, who sustained serious leg wounds in Syria, was in a "stable" condition, the source added.
French President Nicolas Sarkozy announced on Thursday that the two journalists had been safely evacuated from Homs as regime forces overran the city's rebel Baba Amr neighbourhood ending a nearly four-week pounding.
"Edith Bouvier and William Daniels are currently safe on Lebanese territory and will within moments be under the protection of our embassy in Beirut," Sarkozy said during a brief news conference on the sidelines of an EU summit in Brussels.
"I have just spoken with Edith Bouvier, who is naturally exhausted, having suffered hugely but she knows she is free and that she will soon be taken care of," said Sarkozy.
"I want to thank all those who contributed to this happy ending after a week of efforts to evacuate them involving the International Red Cross and the Syrian Red Cross, which didn't succeed," he added.
Le Figaro reporter Bouvier has multiple fractures from a February 22 rocket attack on a makeshift media centre in Baba Amr, a rebel stronghold in the central Syrian city of Homs, in which US veteran reporter Marie Colvin and French photographer Remi Ochlik were killed.
Photographer Daniels was also on assignment for Le Figaro, and was trapped alongside Spaniard Javier Espinosa of El Mundo daily.
The Spanish daily said Espinosa had safely escaped to Beirut, despite claims in Syria that his body had been found alongside those of Colvin and Ochlik.
Another journalist wounded in the attack, British photographer Paul Conroy, was evacuated to Lebanon on Tuesday.