Hariri and his Western-backed March 14 slate secured a victory in the June 7 parliamentary elections and is now tasked with forming the next government.
French officials had emphasized their support for the Lebanese political process while pledging to respect Lebanese independence.
French President Nicolas Sarkozy, for his part, praised his Syrian counterpart Bashar Assad on his support for political integrity in Lebanon.
Analysts had expressed concern over the ability of Lebanon to move forward with forming a national government. The matter is hampered by disputes between the March 14 slate and the March 8 opposition group, which includes the Lebanese Hezbollah.
Kouchner said he would consider the viewpoints of all Lebanese political factions, including Hezbollah.
Meanwhile, opposition lawmakers continued to squabble over a "blocking third" veto power for minority slates, a sticking point in the formulation of the next government.
March 14 members had said no such provision would be extended to minority parties.
Notable deaths of 2014 [PHOTOS]