Le Drian was to meet Saudi Arabia's Crown Prince Mohammed bin Salman on Wednesday evening to discuss "all possible ways of resolving the present situation", Prime Minister Edouard Philippe told parliament on Tuesday.
Philippe called for Hariri, who announced his resignation after apparently being sumlmoned to Riyadh on 4 November, to be able to "freely return" to his country to "clarify his situation in accordance with the Lebanese constitution".
Macron made the same appeal while receiving Lebanese Foreign Affairs Minister Gebran Bassil at the Elysée presidential palace on Tuesday.
Bassil "thanked France for its support for the Lebanese people and its active role in the crisis" and insisted on the necessity of Saad Hariri being able to go to Beirut in the next few days to make his resignation official, if he wishes it", an Elysée statement said.
"Saad Hariri is in an ambiguous and abnormal situation," Bassil said on leaving the Elysée.
Hariri said he would be returning to Beirut within the next two days in a tweet on Tuesday.
Lebanese President Michel Aoun said he considered that Hariri was being held against his will in a tweet on Wednesday morning.
The situation was a human rights violation and the country could not wait indefinitely for the prime minister's return because the state much continue to function, he said.
The French president met Crown Prince Mohammed during a surprise visit to Riyadh while he was in the Middle East last week.
When announcing his resignation, Hariri accused Iran of sowing "sedition, devastation and destruction" in Lebanon, attacked the Shia-Muslim-based Hezbollah movement of being Tehran's "arm, not only in Lebanon but also in Arab countries" and said he feared for his life.
Hariri's father, Rafik, was killed by a car bomb in 2004.
France, which held the League of Nations mandate over Syria and Lebanon after the break-up of the Ottoman Empire following World War I, has contacts with all the country's confessional communities and political players.
Analysts say Macron intends to play a role in the crisis given US President Donald Trump's overt support for Crown Prince Mohammed's intention to counter Iranian influence and weaken Hezbollah with Israel's backing.
Former foreign affairs minister and prime minister Alain Juppé, a member of the opposition Republicans party, praised Macron's initiative this week.
"It's good that the president is rolling up his sleeves and playing the role of mediator," he said. "Perhaps that could work."