The Muslim umbrella group CFCM has called on mosques throughout France to invite non-Muslims to visit on 9-10 January to drink tea, eat sweets and "ask all the
questions they want, even the most taboo, about our religion", its president Anouar Kbibech said on Saturday.
Some mosques staged open days at the time and the CFCM wants the initiative to be nationwide in 2016.
The call comes six weeks after the 13 November Paris attacks, in which 130 people died, and the day after a mob trashed a prayer room in the Corsican regional capital, Ajaccio, following an attack on firefighters and a police officer.
Associating Islam with the assaults on the firefighters was "unbearable", Kbibech told the AFP news agency on Saturday.
Ajaccio mayor Laurent Marcangeli told France Info radio that he was not surprised by the violence.
"I've felt the tension rising for several months," he said, while insisting that the "thugs" who attacked the fire engine made no religious demands.
A dozen Muslims formed a symbolic human shield against possible terror attack on a church in northern France on Christmas day.
The priest of the church in Lens gave them the light of Bethlehem, a Christian symbol of peace.
The government had tightened security at places of worship on Christmas day in the aftermath of the 13 November attacks.