In Clermont-Ferrand, a bomb-disposal operation was called in to sweep the home of a 37-year-old suspect for explosives, a source said.
"The suspects had a plot that was sufficiently advanced for the police to decide to arrest them," another source said.
The raids were ordered by anti-terrorism prosecutors in Paris, according to a judicial source.
France, which has been rocked by a wave of deadly jihadist attacks from January 2015, remains on high alert.
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He was shot and seriously injured by one of the soldiers.
A week later, police arrested four people in southern France, including a 16-year-old girl near Montpellier, on suspicion they were planning an "imminent" attack.
During the raid, the officers found ingredients used to make TATP, a highly unstable homemade explosive used in the November 2015 attacks in Paris.
The teenage girl, her partner and an older man described as their mentor were charged with terrorist offences.
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