"With Brazil in shock, France is ready to help the restoration of the National Museum," Le Drian said in a speech at the Louvre Abu Dhabi, which was inaugurated last year.
"Just like the Louvre, it is a symbol of a dialogue of cultures. It is part of humanity's memory that has disappeared in the flames."
The museum has a collection of more than 20 million objects and a library with more than 530,000 books.
It included the 12,000-year-old remains of a woman nicknamed Luiza - the oldest skeleton ever found in the Americas - and the Bendego meteorite, the biggest meteorite in the country discovered in 1784.
Indigenous artefacts that showed how the continent's people lived in pre-colonial times also appear to have been lost.
"This is not just a loss for Brazil, it's a loss for all humanity," Bruno David of France's Museum of National History commented.
The cause of the blaze has not yet been established but government cuts and inadequate fire protection systems have been cited as key factors.
"Many museums are facing budget worries, even here," David said. "Governments put off work and said 'We'll wait'. Fortunately, 95 times out of 100 it doesn't end in the tragedy of losing a heritage. There it hit hard."