The suspects were plotting attacks on Muslim and Jewish worship sites.
The Neo-nazism movement emerged in the post-World War II era, and seeks to revive the far-right ideology of Nazism.
French news outlet, France 24, quoted a source close to the investigation, who confirmed the dismantling of the cell.
The source said that five members of the cell were “close in ideology to the neo-Nazi movement.” The source added that the five members were “charged between September and May” in connection with plans for islamophobic and anti-semitic attacks.
The investigation found that the cell was “developing an ill-defined plot to carry out an attack, likely to target a place of worship.”
The news outlet said that police first arrested a suspect in the southeastern city of Grenoble on weapons charges in September 2018. The investigation led to four more arrests, including two minors.
Counterterrorism agents were tasked with finishing the investigation in January, charging the suspects with terror offences, France 24 said.
A report on Islamophobia in France, National Report 2017, shows that the issue is on the rise.
The report showed that 121 Islamophobic incidents were reported in France in 2017, while 19 Muslim meeting places were shut down by the government.
France has also seen an increased number of cases of anti-Semitic violence.
The Time reported that “ nine out of 10 Jewish students said they experienced anti-Semitism at least once during their studies” in France.