General Jean-Louis Georgelin, 74, died on Friday in the Pyrenees mountain range straddling the France-Spain border, said the prosecutor's office in the southern French city of Foix.
A mountain rescue team deployed to the Mont-Valier peak "discovered the body of a man who has been formally identified as General Georgelin", a spokesman said, adding that an accident was the likely cause.
Notre-Dame has lost "the overseer of its rebirth" and France "one of its great servants", President Emmanuel Macron wrote on Twitter, now rebranded as "X".
Paris mayor Anne Hidalgo hailed Georgelin on the same social media platform for creating "the human and organisational conditions for successfully completing the reconstruction of Notre-Dame".
A five-star general who was the French army's chief-of-staff between 2006 and 2010, Georgelin supervised operations in Ivory Coast, Afghanistan, the Balkans and Lebanon.
In 2020, Macron chose him to lead the complex and expensive reconstruction work on Notre-Dame.
The cathedral, one of the French capital's most famous landmarks, was gutted by a blaze that shocked the world the previous year.
Georgelin, a practising Catholic whose motto was "move forward without procrastinating", said Notre-Dame's new spire would be completed by the end of the year.
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