Ground was broken for the Paris on April 17, 1997. It opened September 1, 1999 with fireworks being shot from the Eiffel tower.
The back legs of the Eiffel Tower actually come down through the ceiling into the middle of the casino floor.
In the film 10.5 Apocalypse the hotel falls and sinks into to sand when Las Vegas sinks due to an earthquake. You can see the Eiffel Tower falling on its side and sinking.
While the United States Post Office, and most people, call the area where the Paris Las Vegas is located "Las Vegas", the hotel (and most of the Las Vegas Strip) is in Paradise township, an unincorporated part of Clark County.