Visitors are being offered hot drinks, pastries, calligraphy demonstrations and discussion during the "open-house" weekend.
The country's leading Muslim body, the French Council of the Muslim Faith (CFCM), seeks to distance mainstream Islam from recent jihadist attacks.
The initiative comes a year after the Charlie Hebdo killings in Paris.
Jihadist gunmen killed 17 people at different Paris sites, including the offices of the satirical Charlie Hebdo magazine and a kosher supermarket.
Marking the anniversary of the killings, President Francois Hollande unveiled a plaque on Saturday in tribute to one of those who died, policewoman Clarissa Jean-Philippe.
France also remembered the four Jewish hostages killed at the supermarket.
France is still under a state of emergency after November's Paris attacks, carried out by gunmen linked to the Islamic State group, which killed 130 people.
Hundreds of French mosques are taking part in the open-house event, dubbed a "brotherly cup of tea".
"The objective is to create a space where people can be together and meet normal Muslim worshippers and all of our fellow citizens," CFCM President Anouar Kbibech told AFP.
He said the CFCM wanted to use the anniversary of the Charlie Hebdo attacks to "highlight the real values of Islam, to set straight the cliches about links to violence and terrorism".
French mosques have invited non-Muslims in to try to create greater understanding of Islam in France.