The arrests of suspects aged 17-25 were made in the Paris region and southeast France as part of an investigation into far-right activists, the
The nine men and one woman are suspected of links to 21-year-old Logan Alexandre Nisin, a former militant of the far-right group Action Francaise Provence who was arrested in June, the source said.
One source said the woman arrested Tuesday is Nisin's mother.
Police investigations had unmasked "intentions to commit violent action" of which the details remained unclear, a judicial source said, but that involved "a place of worship, a politician, a migrant, drug trafficking".
Another source named the targeted politicians as government spokesman Christophe Castaner and radical left leader Jean-Luc Melenchon.
A Melenchon spokesman complained that the former presidential candidate "was not informed and requests for protection during the legislative elections was rejected".
The suspects, taken into custody for "association with terrorist wrongdoers", were also thought to be plotting to target migrants as well as mosques.
"They were only in the earliest planning stages," one source said.
Nisin was arrested near Marseille on June 28 after posting that he planned to attack blacks, jihadists, migrants and "scum".
One of the probe sources said investigators had determined that Nisin, who possessed arms and practised shooting, had the intention of following through with his threats.
Nisin came to the attention of the French authorities as the administrator of a Facebook page glorifying neo-Nazi Anders Behring Breivik, who killed 77
people in a bomb and gun rampage in 2011 in Norway.
Action Francaise describes itself as a "royalist" organisation and held a meeting in a Marseille street at the weekend. A rival demonstration by anti-fascists was also held nearby and resulted in clashes between he two groups.
Liberation newspaper reported how riot police had to intervene to separate the two groups.