According to newspaper Le Parisien, Mrs Chirac's 62-year-old brother and his 22-year-old daughter were subjected to kicks and blows by a group of eight young people.
The attack happened at around 11pm at the Champs-Elysées-Clemenceau station on line 1 of the metro system.
The newspaper reports that Jérôme Chodron de Courcel was with his wife and their daughter, Emma, on line 1 of the metro on Wednesday evening at about 11pm. When the train arrived at the Champs-Elysées-Clemenceau station a group of young people aged between 18 and 21 boarded the train.
According to witnesses, one of the young people kicked the brother of Bernadette Chirac, who struck back with a punch. The incident then degenerated as the three were subjected to kicks and blows by the group.
"The father received several blows to the face while his daughter tried to intervene," said one source quoted by Le Parisien. "Several young men in the group attacked them."
Several other passengers tried to help, including Jack Lang, the former Socialist culture minister who happened to be on board the same train.
"He was present at the time of the incident," confirmed his office, adding that he had got involved to help.
The victims were treated by transport police who managed to catch five of the eight attackers. They are now being held for questioning.