The novelisation refers to the "War against the Southern Territories".
This was the army humanity had fronted in one of the worst wars of its
entire checkered history—the War against the Southern Territories. It
was largely because of this war, with its years of violence and
astronomical numbers of casualties on both sides, that humanity had
firmly rededicated itself to pursuing peace if at all possible. Peace
bought with the bloodiest of prices, Okto-Bar remembered his father
saying. He continued to read the list of ships and their captains.
Valerian and the City of a Thousand Planets: The Official Movie Novelization
And the film itself identifies the baddies (over Mül) as being "the Arysum-Kormn"
The war against the Arysum-Kormn led to the destruction of Planet Mül.

Nothing more specific is known other than that humanity won, and was so horrified by the death and destruction that it then dedicated itself to the cause of galactic peace.