The shots of the Betty landing on Earth were cut from the theatrical version of Alien Resurrection before the special effects for them were finished. The footage was only completed when the extended Special Edition was compiled for release in 2003. It is likely the use of a devastated Paris as a setting was a choice made by the film's director director Jean-Pierre Jeunet, who is French.
In the comic Aliens vs. Predator vs. The Terminator, which is an unofficial sequel to Alien Resurrection, it is explained that the devastation of Earth seen in the Special Edition of Alien Resurrection was the result of the war between mankind and Skynet and its Terminators. Paris was destroyed either in the nuclear holocaust, known as "Judgment Day", that initiated the war, or during the subsequent fighting with the machines.