The sale is part of a strategy to sell state assets worth up to €10 billion over the next 18 months.
A consortium made up of Chinese companies Shandong Hi-Speed Group and Friedmann Pacific Asset Management made the winning bid for the stake, the French Economy Ministry has said, which was sold for €308 million.
The gateway was put up for sale in July, and attracted interest from companies including Australia's Macquarie, Spain's Ferrovial, France's Vinci together with CDC Infrastructure and EDF Invest and French airport operator ADP along with insurer Predica.
The French state, which had owned 60% of the airport, has an option to sell its remaining 10.01% stake, but currently does not intend to exercise it, the ministry adds.
The airport is the biggest in southwestern France and handled more than 7.5 million passengers in 2013, generating revenue of €117.4 million and net profit of €10.6 million.