Two men aged 56 and 29, and a 53-year-old woman were among six people arrested on Tuesday during raids in Haguenau in eastern France and 200 kilometres further south in Sochaux.
The other three were released after questioning, police said on Saturday.
It is understood French secret services uncovered the group as they tracked religious and left wing extremists.
Officers from the Directorate General of Internal Security have foiled several planned attacks by rightwing extremists since 2017, most notably a plot to target President Emmanuel Macron in November 2018.
