Alain Robert climbed up the 38-floor-building (144 meters) using just his bare hands in around 20 minutes.
Spanish authorities briefly detained him after the stunt.
Mr Robert said he wanted to bring attention to what he described as the "paranoia" around the coronavirus.
"The problem is fear is more contagious than virus itself," he said.
At least four people have died from Covid-19 and more than 200 people have been infected by it.
France borders Italy which has had the highest number of coronavirus deaths outside of China - 107 and at least 3,089 people have tested positive for the illness.
Worldwide, more than 93,000 people have been infected and over 3,100 have died, the vast majority in China.