I copied every music of Deus Ex from its "Music" folder. However, I couldn't find the music can be heard on the streets of Paris, even though I can hear that ingame.
Which UMX file contains that? I could notice while playing them with VLC media player that these files contain certain chillout music, battle music, end music and dialogue music the same file.
(for making the question clearer, this is the music I'm talking about – thanks for Brant for warning)
Best Answer
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).