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The suspects, two men aged 29 and 56 and a 53-year-old woman, were indicted on Friday evening by a Paris anti-terrorist judge on suspicion of forming a "terrorist criminal association", the source added.
Three others also arrested on Tuesday — two men and a woman — have since been released.
Belonging to a group calling itself "Honour and Nation", the suspects are believed to have planned a violent attack, although they were not on the verge of carrying it out, a source familiar with the investigation said.
They were arrested based on their communications, research into explosives and scouting of the potential target.
The probe is just the latest into France's far-right scene.
Last month anti-terror prosecutors requested a trial for nine members of a group calling itself OAS that was dismantled in 2017, suspected of targeting senior politicians or French Muslims.
Another organisation suspected of planning attacks on Muslims, AFO, was taken down in 2018, the same year as still another group believed to have been preparing an attempt on President Emmanuel Macron's life.
Further anti-terrorist probes relate to a neo-Nazi group suspected of targeting Jewish and Muslim places of worship and to a white supremacist who admired the perpetrator of the 2019 attack on mosques in New Zealand city Christchurch.
"I want the world to know who Atta Elayyan was," said 27-year-old Farah Talal, dressed in a green djellaba robe and an elegant white scarf during her visit to Islam's holiest city.
A lone gunman used a semi-automatic gun to kill worshippers gathered for Friday prayers at two mosques in the city of Christchurch on March 15 last year in New Zealand's worst peace-time shooting.
Outside the Al Noor mosque, dozens of leather-clad bikers from the Tu Tangata club performed a traditional Maori haka. They were welcomed by mosque imam Gamal Fouda, who said people of all beliefs and cultures were stopping to pay their respects, and they were all united as New Zealanders.
"This setting will be the new default for people who don't already have the SafeSearch filter turned on, with the option to adjust settings at any time," the company said.
Last month, the government had raised the price of petrol and diesel by 35 PKR per litre each, a couple of days before the scheduled date of revising oil prices, apparently bowing to hoarders rather than taking action against them, The Express Tribune reported.
Heartrending scenes of a newborn plucked alive from the rubble and a broken father clutching his dead daughter's hand have laid bare the human cost of violent earthquakes in Syria and Turkey that by Wednesday had claimed 7,800 lives.
The last two days have brought dramatic rescues, including small children emerging from mounds of debris more than 30 hours after Monday's pre-dawn quake. But there was also widespread despair and growing anger at the slow pace of rescue efforts in some areas.