Architects working on preserving Notre-Dame are rushing to cover the cathedral before rain can cause further damage.
Showers and even possible thunderstorms are forecast for the French capital on Tuesday evening.
The cathedral's vault, which partly collapsed in the fire, is already partly waterlogged after fire-fighting efforts.
Architects fear that heavy rainfall could result in further collapse.
The chief architect of Notre-Dame , Philippe Villeneuve, told French broadcaster BFMTV that erecting an emergency tarpaulin was "the highest priority".
"The beams are there, the tarpaulin is arriving. The climbers, since it will be climbers who will do that, and the scaffolders, are ready," he said.
There are already plans to erect a large, purpose-built "umbrella" on the roof of the landmark, which will have its own peak and protect the structure while reconstruction takes place.
But the umbrella is not ready - and the threat of impending rain is too serious to wait, with even heavier rain forecast for Thursday.
There were fears the 800-year-old cathedral could be completely destroyed during the fierce blaze on 15 April. Firefighters managed to save the structure and much of its interior - but emergency work has been taking place since to stabilise the building.
Three large holes in the cathedral's vault - its arched ceiling - are the most obvious signs of damage. One was made by the collapse of the cathedral's spire.
But its famous rosette stained-glass windows have been covered with protective material and reinforced with timber posts.
What next for Notre-Dame?
French President Emmanuel Macron has vowed to rebuild the symbol of Paris within five years - in time for the Olympics in the city scheduled for 2024.
The cost is likely to be enormous, with hundreds of millions already pledged by individuals and businesses both in France and from around the world.
Prime Minister Édouard Philippe has suggested an international competition for designs for the new spire, to replace the 19th-century design by Eugene Viollet-le-Duc which collapsed.
In the meantime, however, plans are in motion to build a temporary wooden cathedral in the square outside to continue Catholic services on the grounds. The idea which has already earned the approval of Paris mayor Anne Hidalgo.
Notre Dame was already undergoing extensive restoration work when the fire broke out. It is not yet clear if that contributed to the blaze, or what the cause was.
Alongside protecting the cathedral from the rain, the removal of the damaged scaffolding is one of the first steps towards the cathedral's full restoration - a process that could take weeks.