"What happened tonight in Paris, in this Cathedral, is a terrible event," the President said, vowing to raise funds worldwide and bring the best talents from around the world to reconstruct the building in its entirety.
"Notre Dame is our history, our literature, part of our psyche, the place of all our great events, our epidemics, our wars, our liberations, the epicentre of our lives... So I solemnly say tonight we will rebuild it together.
"Starting tomorrow, a national donation scheme will be started that will extend beyond our borders," he added.
The fire began at around 6.30 p.m., on Monday and quickly caused the collapse of the Cathedral's spectacular Gothic spire and the destruction of its roof structure, which dated back to the 13th century.
Consumed by flames, the spire leaned to one side and fell onto the burning roof as horrified onlookers watched.
The massive blaze was brought under control by some 500 firefighters in the early hours of Tuesday morning, though officials warned there were still residual fires to put out which could take several days to completely extinguish it.
The cause of the fire is not yet clear but officials believe it could be linked to extensive renovation works under way. The Paris prosecutor's office said it was currently being investigated as an accident.
The 12th-century Cathedral's iconic facade and towers were salvaged, as were a host of invaluable artefacts and works of art stored inside, including the Holy Crown, believed by many to be from the crown of thorns placed on the head of Jesus Christ, and which the cathedral calls its "most precious and most venerated relic".
A tunic, which King Louis IX is said to have worn when he brought the crown of thorns to Paris, was also saved.
"We had a chain of solidarity, especially in saving the works of art... (They) were able to be saved and put in a safe place," said Paris Mayor Anne Hidalgo.
Thousands of people gathered in the streets around the Cathedral, observing the flames in silence. Some could be seen openly weeping, while others sang hymns or said prayers.
Several churches around Paris rang their bells in response to the blaze, which happened as Catholics celebrate Holy Week.
Messages of support and mourning poured in from around the world.
The Vatican said the Holy See learned with "shock and sadness the news of the terrible fire that has devastated the Cathedral of Notre Dame de Paris, symbol of Christianity, in France and in the world".
The fire at the Notre Dame cathedral "goes beyond Paris", the city's archbishop, Michel Christian Alain Aupetit, told CNN.
US President Donald Trump called it a "terrible, terrible fire", while the Unesco said it stood "at France's side to save and restore this priceless heritage" visited by almost 13 million visitors each year, more than the Eiffel Tower.
German Chancellor Angela Merkel called the Notre-Dame a "symbol of French and European culture".
UK Prime Minister Theresa May said in a tweet "My thoughts are with the people of France tonight and with the emergency services who are fighting the terrible blaze at Notre-Dame cathedral."
UN General Secretary Antonio Guterres said "Horrified by the pictures coming from Paris with the fire engulfing Notre Dame Cathedral - a unique example of world heritage that has stood tall since the 14th century..."
The Notre Dame's foundation stone was laid in 1163 by Pope Alexander III, and the Cathedral was completed in the 13th century.
Today, with its towers, spire, flying buttresses and stained glass, Notre Dame is considered a feat of architecture as well as a major religious and cultural symbol of France. It is one of Paris' most popular attractions, drawing an estimated 13 million visitors a year.
It was the site of Napoleon Bonaparte's coronation as Emperor in 1804. The central spire was built in the 19th century amid a broad restoration effort, partly buoyed by the success of Victor Hugo's novel "The Hunchback of Notre-Dame" in 1831.
The Cathedral also houses the grand organ, one of the world's most famous musical instruments, as well as the Crown of Thorns, a relic of the passion of Christ.