The six players are all with France's Grenoble club. French media reports said the New Zealanders were former Sevens and Waikato player Rory Grice and former Marlbrough player Dylan Hayes.
Grenoble newspaper Le Dauphine Libere said it had spoken to Grice's layer, Philip Fitzgerald, who said Grice was "anxious to answer police questions about the case". He reminded the newspaper to remember the presumption of innocence.
Mr Fitzgerald said Grice remained in custody.
Hayes had left the police station, according to this lawyer, the newspaper said.