I’ve always heard it spoke G-I-G-N, each letter said. It’s an abbreviation for Groupe d'intervention de la Gendarmerie nationale. National Gendarmerie Intervention Group.
There is another movie about their retaking of a hijacked airliner and rescuing of the hostages. There’s a bit of revolver use by the GIGN members.
The movie is called The Assault, here’s a clip from it with the revolvers https://youtu.be/aveIcPFjuCM