Police officials who declined to be named told the French news agency they were involved with Ekta Parishad, a charity that says it is a non-violent activists movement working for local people's land, water and forest rights.
The group, including six women, were ejected from the eastern state for breaching restrictions on their tourist visas, police said, though officers were unable to confirm whether the ten would be deported from India.
The presence of foreigners in remote areas of India controlled by the Maoists is sensitive after two Italian men were abducted last month by the rebels in the state of Orissa. They were both later released unharmed.
India's Maoist guerrillas, who claim to be fighting for the rights of poor tribals and farmers, have waged a decades-long battle across central and eastern states to overthrow state and national authorities.
They often target police and government officials in deadly ambushes and mine attacks. In their latest major strike, they killed 11 policemen in a landmine blast in Maharashtra last month.
The French group are thought to have arrived in India earlier this month and travelled to Bihar after visiting south India. One was reported to be on an employment visa.
According to the Hindustan Times, they were detained on Saturday and taken under police escort to the state capital Bihar on Sunday to catch a flight to Kolkata.