Nine men and one woman aged 32 to 69 were arrested in raids across France on Saturday.
The suspects, whose detention was extended late Monday for a further 48 hours, had an "ill-defined plan to commit a violent act targeting people of the Muslim faith.” Police have linked the ten to a little-known group called Action des Forces Operationnelles (Operational Forces Action), which urges French people to combat Muslims, or what it calls "the enemy within".
Rifles, handguns and homemade grenades were found during searches in the Paris area, the Mediterranean island of Corsica and the western Charentes-Maritimes region.
The group's suspected leader, identified as Guy S., was a monitor for the far-right National Front during last year's presidential and legislative elections, according to the mayor of the western town of Tonnay-Charente.
But a local official for the party, since rebaptised the National Rally, said the man, a retired police officer, did not figure on party membership lists and was not among the party's known "supporters".
Party leader Marine Le Pen welcomed the arrests, saying "any terrorist attack targeting people must obviously be repelled with the utmost force."
'War for France'
France remains on high alert following a wave of jihadist attacks which have killed more than 240 people since 2015.
Officials have urged people not to confuse the actions of radicalised individuals with those of France's estimated six million Muslims -- but anti-Islamic violence is on the rise.
The "Guerre de France" (War for France) website of the shadowy Operational Forces Action depicts an apocalyptic battle scene under the Eiffel Tower, and claims to prepare "French citizen-soldiers for combat on national territory".
France's TF1 television said the group planned to target radicalised imams and Islamist prisoners after their release from jail, as well as veiled women in the street chosen at random.
France registered 72 violent anti-Muslim acts last year, up from 67 in 2016.
"I'm not surprised by these arrests because the current climate of Islamophobia encourages this sort of passage from words to deeds," said Abdallah Zekri of the French Council of the Muslim Faith.
The Council said it was particularly worried about the security of the country's roughly 2,500 mosques.
In a statement, Interior Minister Gerard Collomb emphasised the "total mobilisation" of security services "to prevent any disturbance to public order and any threat to people and property, especially those targeting a particular religion."