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".

It follows the discovery of 115 people locked inside three small houses in Edinburg, close to the Mexican border.
Police were alerted by a call made from inside one of the houses. The property was found to have padlocks and chains on the outside.
People found inside said they had not had any food or water for three days, and some required hospital treatment.
Oscar Trevino, an Edinburg police spokesman, told the BBC that it was clear the people in the properties were being held against their will.
"There was no way that they could leave because the doors were secured with burglar bars and were locked from the outside."
He said officers had to use bolt cutters to free those inside.
The imprisoned people came from several different countries in south and central America.
One man told officers that they had been driven to the houses from the Rio Grande river, which marks the border between Texas and Mexico.
He said they had been threatened with death if they did not remain quiet.
French mosques have invited non-Muslims in to try to create greater understanding of Islam in France.
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