The petition demands that President Emmanuel Macron withdraw his loan offer, which is described as "a cultural heritage crime".
The central issue is whether the 900-year-old tapestry, a priceless work of art from the Middle Ages, can withstand transport or not.
Also, museum advisor Cécile Binet, at the regional directorate for cultural affairs in Normandy, says that the tapestry is "too fragile to be moved over long distances".
It is not impossible to transport, says Phillie Bélaval, former cultural advisor to President Macron and now responsible for the loan, to AFP.
According to him, the transport will likely take place by truck. He refers to an "extremely careful study" that detailed shows how a transport should be carried out.