Production sharing contracts were awarded to Total during a licensing round last year. The two blocks cover a collective offshore area of 2,135 square miles in water as deep as 8,200 feet.
Arnaud Breuillac, a vice president in charge of regional exploration and production, said the acquisition is in line with the company's growth ambitions in the Mediterranean region. Exploration work is expected to begin with seismic surveys.
Cyprus may hold more than 10 trillion cubic feet of natural gas reserves offshore, though the area may be a source of contention given regional rows between the Cypriot and Turkish governments.
Cyprus is considered frontier energy territory. Total gave no estimate about it reserve expectations from the two offshore blocks.
Last month, Italian company Eni made its debut in Cyprus with three deep-water blocks that cover about 4,800 square miles in the Levantine basin.