Other countries offered help. At Windsor and York Minster, both victims of crippling fires, British experts said they would help Notre Dame rise from the flames. Vladimir Putin, the Russian President, said he was ready to send the "best specialists" to rebuild it. The President of Poland said his country could help because of its experience rising from the rubble of World War II.
And among the shared grief, a glint of hope. It emerged that an architectural historian, Andrew Tallon, completed a little-known project three years ago that may prove key to restoring Notre-Dame's roof.
Over months and years, the Belgian-born academic, who died last year aged 49, laser-mapped nearly every inch of the cathedral, using billions of points of light.
The task will not be simple, however.
The cathedral's oak roof is nearly completely destroyed, while stone walls that stood for 800 years are thought to have been cracked by the heat, and may no longer be safe.
Many of its treasures were saved by firemen, but others were lost to the flames or damaged by smoke and water, perhaps beyond repair.
The question now facing French authorities is what to do next.
The walls
Despite the intense blaze, the famous twin bell towers are still standing.
Behind them, however, the main body of the cathedral has been left dangerously unstable.
The cathedral is "under permanent surveillance because it can still budge," Christophe Castaner, the French Interior Minister, told reporters after a brief visit inside.
"We will be standing at her bedside," he said.
Dumping cold water on red hot stone can cause it to shatter and crack, while extreme temperatures can cause calcination, a process that turns stone into powder.
Until the building is made safe, no restoration work can be done. This could take months, or even years, experts said.
The building is already wet through from the water pumped in by firefighters. Without a roof, the timber and masonry is exposed to the elements, so a temporary cover will be needed.
The blackened scaffolding, which withstood the fire and remains in place, is also a concern. It could collapse, and will take time to remove.
The roof
It took just over an hour for the 800-year-old timbers holding up Notre Dame's roof to be consumed by fire.
The safest option may be to rebuild them out of fireproof concrete, as used at Reims Cathedral after it was set on fire during World War 1.
Experts said today, however, that Notre-Dame's wooden beams will most likely be replaced.
John David, a master mason at York Minster who helped rebuild it after a devastating fire in 1984, said he and his team were on hand to help.
"I think they'll replace the beams," he said. "That's what we did, and it was the right choice. We've put fire breaks in there to reduce the risk. But you've got to use craftsmanship to rebuild Notre Dame. You can't build the thing out of concrete."
Francois-Henri Pinault, Kering's chief executive, agreed, insisting that the intricate lattice woodwork supporting the roof that was lost in the blaze had to be replicated.
"This is why it's going to be long, extensive, but we have to do it," he said.
The project faces another hurdle. Europe is no longer blessed with forests of giant oaks, ready to be chopped down. More than 1300 oak trees were used for Notre-Dame's orginal roof frame, equivalent to 20ha of woodland.
Bertrand de Feydeau, vice-president of preservation group Fondation du Patrimoine, said the cathedral's roof cannot be rebuilt exactly as it was before the fire because "we don't, at the moment, have trees on our territory of the size that were cut in the 13th century".
Thousands of private forest owners pledged yesterday to donate one oak each to the new roof.
"The French timber industry is going to organise itself to supply French oak, and will participate, including financially, in the reconstruction of the cathedral," said Michel Druilhe, president of the France Bois Forêt group.
The treasures
A frantic rescue effort saved the monument's "most precious treasures," including the Crown of Thorns purportedly worn by Jesus.
Also surviving was the Roman Catholic cathedral's famous 18th-century organ, which boasts more than 8000 pipes. Sixteen statues removed from the roof for restoration just days ago also were safe.
Other works have been taken from City Hall to the Louvre museum. There they will be dried, protected and eventually restored. One official said the cathedral's greatest paintings, most from the 18th century, would be removed starting this weekend.
"We assume they have not been damaged by the fire but there will eventually be damage from the smoke," he added.
The three large stained-glass rose windows, among the most famous elements inside the cathedral, have not been destroyed, but may have been damaged by the heat, and will be assessed by experts.
The cathedral also houses an important collection of statues, including figures of Old Testament kings that stand above the entrance. Their condition was not clear.
The organ, though intact, is "a very fragile instrument, especially its pipes," and its condition is still of concern, an official said.
"It has not burnt, but no one can tell whether it has been damaged by water. Nobody knows if it is a functioning state or will need to be restored,"they added.
According to one scientist, the organ's famous sound may never be the same again.
"The fire damage to the roof of the building means that it can no longer make those same responses to sound that it has been making for over 800 years, which is tragic indeed," said Dr Jez Wells, from the University of York's department of music.
