When the Islamic State was about to be driven out of the ancient city of Palmyra in March, Yves Ubelmann got a call from Syria’s director of antiquities to come over in a hurry.

An architect by training, Mr. Ubelmann, 36, had worked in Syria before the country was engulfed by war. But now there was special urgency for the kind of work his youthful team of architects, mathematicians and designers did from their cramped offices in Paris: producing digital copies of threatened historical sites.

Palmyra, parts of it already destroyed by the Islamists who deemed these monuments idolatrous, was still rigged with explosives. So he and Houmam Saad, his Syrian colleague, spent four days flying a drone with a robot camera over the crumbled arches and temples.