The officer, who has not been named in the reports, was suspended from the team guarding Charlie Hebdo chief editor urent "Riss" Sourisseau last month after a routine check of personnel, BFMTV says.
He has also had his gun confiscated.
He has appealed against the move.
The investigation found that the man, a Muslim, consulted Islamist websites while he was responsible for the protection of Hassen Chalgoumi, the imam of a mosque in Drancy, near Paris, known for his opposition to fundamentalism.
Some of his colleagues also reported behaviour and contacts they considered "worrying".
A "highly placed" source told BFMTV that, although the activity did not mean he was a terrorist, it was "abnormal" and "incompatible with the close protection of well-known people".
In January 2015 Chérif Kouachi and Saïd Kouachi attacked Charlie Hebdo's office,killing 12 people and injuring 11 others.
The paper had been attacked before after publishing cartoons depicting the Prophet Muhammad and has continued to receive threats.