Where's the "Paris Streets" soundtrack in Deus Ex's folder?
The song we can hear on the streets of Paris (linked in OP) can be found in the ParisCathedral_Music.umx file in the music folder of Deus Ex. This file starts playing the music can be heard on the Payens Cathedral level. After that, around 2:27, the Paris Streets music comes.
Most certainly, when selecting music (combat mode, new levels, etc.), the game jumps between files and goes to a given mm:ss part - that's how is it possible, and that's why one UMX file contains several music (including dialouge and combat music after the main ambient music).