The bids from Panama-registered NetOil and Libya's Murzuq Oil are expected to be considered in the coming days, ahead of an April 16th deadline.
Unions representing the plant's 470 workers hailed the decision.
"This is very good news," said Jean-Luc Broute of the CGT union following a meeting of the plant's works council.
Two other bids, from Hong Kong-based Oceanmed Seasky System Limited and GTSA of Luxembourg, were rejected.
Opened in 1929, the refinery has struggled in recent years, with parent company Petroplus filing for bankruptcy in January 2012 and the plant placed under insolvency administration in October.
The fate of the plant has become a symbol of France's struggle to keep industrial sites running in the face of a stagnant economy and stiff global competition.