Huguette Dupeu – one of the French citizens wounded during the Islamic State attack on Tunisia's National Bardo Museum on 18 March – has died.
She was hospitalised in the Tunisian capital, Tunis, following the incident. Her death brings the death toll from the terrorist shooting to 22.
A statement from President Hollande's office said: "The President of the Republic expresses his deep sadness following the death in Tunis of Mrs Huguette Dupeu who was seriously injured".
Tourists from Britain, Italy, Japan, Spain, Belgium, Poland, Russia, Colombia and Australia were also killed by the gunmen.
The country's tourism sector has taken a heavy hit following the 2011 revolution which led to the overthrow of President Zine El Abidine Ben Ali and sparked the Arab Spring. Travel and tourism accounts for 15.2% of the country's GDP and many visitors come from France.
The Islamic State (Isis) has claimed responsibility for the attack, but the Tunisian government has identified the involvement of fighters from Okba Ibn Nafaa Brigade – a local group linked to al-Qaeda, which is based near the Algerian border.
More than 20 people have been arrested in connection with the attack, although only two gunmen – who are thought to have been trained in an IS-controlled area of Libya – carried out the attack.
President Hollande is set to pay tribute to the victims of the attack later today by attending a "march against terrorism" alongside other world leaders and thousands of local people.
Tunisian President Beji Caid Essebsi and Italian Prime Minister Matteo Renzi will also participate in the march, which will begin at Bab Saadoun Square and conclude outside Bardo Museum.
Tunisian Prime Minister Habib Essid has dismissed seven police chiefs over the incident.