The North African country has two rival governments, one in the east and a UN-backed administration in the capital Tripoli in the west, in a conflict stemming from the overthrow of Muammar Gaddafi in 2011.
France was a leading player in the NATO intervention against Gaddafi, sending warplanes to bomb his forces.
The United Nations launched a new round of talks in September in Tunis between the rival factions to prepare for presidential and parliamentary elections in 2018, but they broke off after one month.
"I noted the desire from the Prime Minister (Fayez al-Seraj) to stick to the calendar. We have a total convergence of views to implement this agenda," Le Drian said after meeting the Tripoli-based prime minister in the Libyan capital.
Drian was later to fly to the eastern city of Benghazi to meet the powerful eastern military commander Khalifa Haftar, who on Sunday called the UN-backed government and peace process obsolete.
The UN talks had stumbled over the question of what role Haftar should play. He indicated on Sunday he wanted to run as presidential candidate.
Haftar remains popular among Libyans in the east who are weary of the chaos, but faces opposition in western Libya.
The eastern-based House of Representatives on Tuesday widened divisions between the east and the west by approving a new central bank governor. The bank's Tripoli headquarters and the UN rejected the move.
Le Drian said a political deal would help solve the crisis of thousands of illegal migrants stuck in detention centers in Libya where human rights groups said they often faced abuse. Libyan officials deny this, but say they are overwhelmed with a flood of migrants.
Libya is the main departure point for illegal migrants heading for Europe by boat.