Lebanese Prime Minister
Hariri has been in Riyadh since announcing his shock resignation from there on November 4, and Lebanon's President Michel Aoun on Wednesday accused Saudi authorities of "detaining" the premier.
"We hope that the crisis is over and Hariri's acceptance of the invitation to go to France is the start of a solution," Aoun said on the official presidential Twitter account.
"I am awaiting the return of Prime Minister Hariri from Paris for us to decide the next step with regards to the government," Aoun added.
Hariri has not returned to Lebanon since he announced he was standing down, and Aoun has yet to accept the resignation, saying he was waiting for the premier to return to Lebanon.
In his sharply worded resignation statement, Hariri, 47, accused Saudi Arabia's arch-rival Iran and its Lebanese ally Hezbollah of destabilising his country and the broader region.
Speculation has swirled around the fate of Hariri, who is a dual Saudi citizen.
On Wednesday, Aoun accused Saudi Arabia of "detaining" Hariri after what he said was his failure to return to the country for 12 days.
"We consider him to be held and detained, contrary to the Vienna Convention," he said.
On Thursday, French Foreign Minister Jean-Yves Le Drian said during a visit to the kingdom that Hariri would travel to France.
"He will come to France and the prince has been informed," Le Drian told reporters, referring to Saudi Crown Prince Mohammed Bin Salman with whom he held talks the previous evening.
The French president's office said on Wednesday that Hariri and his family had been invited to France for a "few days" but that did not mean he would stay there in exile.
Macron has stressed that Hariri should be able to return to Lebanon to confirm or withdraw his resignation in person.
On Wednesday night, Okab Sakr, a close adviser of Hariri's, told the Lebanese television station MTV that the premier "will leave in 48 hours for France with his family".
He added that Hariri would return to Lebanon, but without specifying when.