The scuffle broke out in the airport's Hall 1 on Wednesday, with witnesses swiftly spreading videos of the incident on social networks. The West Hall 1 had to be briefly closed, which led to delays for several flights.
The airline confirmed to French newspaper Le Parisien that it was bringing legal action "because of the impact of these events on its operations."
The Aeroports de Paris, which manages the international airports of the French capital, and the manager of one duty-free store in Orly have already filed complaints.
Both rappers and several members of their posse were taken into custody on Wednesday and their court hearing is expected to take place later on Friday. So far, the two sides have reportedly been blaming the fight on each other.