Officers claim the three men are linked to their chief suspect, Sid Ahmed Ghlam, who was arrested last week after a plan to kill Christians was uncovered.
It is claimed Mr Ghlam, an Algerian living in Paris, was set to target a church in Villejuif, south of Paris.
He is also accused of killing a woman nearby and detectives claim to have found guns and a note with church details in his car.
Police say the three suspects are in custody and that two of the men's DNA was found in Mr Ghlam's home whilst the other is accused of providing logistical support.
Premier understands a search of the suspects home uncovered three Kalashnikov assault rifles and computers showing he had been in contact with jihadis in Syria.
There is no evidence the suspect had ties to any known terrorist organisation.