Catalan separatists have threatened "mass civil disobedience" if Madrid carries out threats to depose their leaders, including Puidgemont, as tensions rise over a bid to sever the region from Spain.
"We feel that Europe has not been playing its role," said Jaume Roure, the head of Unitat Catalana which seeks self determination for French Catalans.
"As the storms are gathering, we have asked people ... to see if they can host the Catalan government and those people who are forced to leave," he said, speaking of Perpignan, the capital of France's Pyrenees-Orientales department which acts as a bridge between Barcelona and the south of France.
The region was for centuries subject to the Crown of Aragon along with Catalonia, and only became French in the latter half of the 17th century.
Several Catalan Republicans fled to this region from Spain during the long dictatorship of General Francisco Franco. The offer from Unitat Catalana came on the anniversary of the return of former Catalan regional president Josep Tarradellas to Barcelona after 38 years in exile.