"The bodies are still in the plane, apart from seven bodies that have been brought up but no identified," France's Francophonie Minister Yamina Benguigui, who has gone to the scene, told the AFP news agency, explaining that it went down in one of the deepest stretches of the River Mekong.
"Apparently it's a question of human error and difficult meteorological conditions," she told BFMTV.
Seven French nationals were among the 49 people on board the Lao Airlines ATR 72-600.
Apart from the 16 Laotian passengers, the passengers came from Australia, Thailand, South Korea, Vietnam, the US, Canada, China, Malaysia and Taiwan.
Thailand's English-language Bangkok Post has published a list of those on board.
They were flying the capital, Vientiane, to the popular tourist destination of Pakse in the south of the country when the plane ran into strong winds that blew it off course just eight kilometres from its destination.
French President François Hollande expressed "great sadness" in a statement.
Lao Airlines runs internal flights as well as flights to China, Thailand, Vietnam and Cambodia.
It carried 900,000 passengers in 2012, compared to 500,000 in 2010, according to the state-owned Vientiane Times, which says that 3.3 million people visited the country last year.
There have been 29 planes crashes that have cost lives in Laos since 1950, according to the Aviation Safety Network, which says that safety had greatly improved recently.