French President Francois Hollande expressed "deep sadness" at the death of Huguette Dupeu in a statement.
Most of the dead in the raid were foreign tourists. Two of the attackers were killed by security forces.
A huge march against terrorism is planned for Sunday that will finish outside the Bardo museum.
President Hollande is among those expected at the event in the capital Tunis.
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The museum's planned reopening earlier this week was postponed over security concerns.
Schoolchildren and students were allowed in on Friday, with the general public to be readmitted Monday.
The attack, claimed by Islamic State (IS), was the deadliest in Tunisia since the uprising which led to the overthrow of long-serving ruler  Zine al-Abidine Ben Ali in 2011.
Over 20 people have been arrested in connection with the attack, although just two gunmen are thought to have carried out the raid.
They are said to have been trained in Libya in an area controlled by IS.
The Tunisian Prime Minister, Habib Essid, has admitted "shortcomings" in the country's security system and has dismissed six police chiefs over the attack.

Ms Tiffney was last seen leaving her home in Edinburgh's Dean Village in May 2002.
A murder charge against her son Sean Flynn was found not proven by a jury at the High Court in Perth in 2005.
The remains were found in an area off the A198, near the entrance to Gosford House in Longniddry.
A cyclist called the emergency services when they made the discovery at about 18:30 on Sunday.
There are 40 police officers working on the find.
It is thought Ms Tiffney was murdered and her body disposed of in the Gosford House area.
The bones are still in situ and it is understood it will take a few days to recover them.
Det Supt Pat Campbell, of Police Scotland, said: "The recovery will be a painstaking process.
"We are consulting with a number of experts to ensure that the remains are recovered in a sensitive and careful manner and no evidence that helps us to establish what happened is damaged or missed.
"I understand the anxiety of those who may be waiting for news of a missing loved one, but whilst the identity of the remains is unknown we cannot speculate."
He added: "The death is being treated as unexplained and once the remains are recovered, there will be significant, detailed forensic analysis required to establish the cause of death and whether any crime has been committed."
A Frenchwoman injured in the attack on Tunisia's national museum has died of her wounds, bringing the total killed in the assault by Islamists to 22.
[NEXT_CONCEPT]
Police investigating the discovery of human remains in East Lothian have spoken to the family of missing woman Louise Tiffney.