NATO took over command of the coalition military intervention in Libya from the United States on Sunday. The mission is trying to ensure a no-fly zone and arms embargo over the country.
The strikes, conducted by two French Rafale fighter patrols, struck the center, located 10 kilometers from Tripoli, on Sunday.
No further strikes were conducted by French forces on Monday, Burkhard said.
Earlier on Monday, France and Britain urged Gaddafi's supporters to "defect before it is too late."
The rebel army, which has been fighting pro-Gaddafi forces since mid-February, has made rapid advancements into the west of Libya since the coalition mission began.