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After the news about their notoriety spread over Europe, the term was used to describe violent street crime in other countries as well: "Russian apaches", etc.
There are a number of stories about the origin of the term "Apaches", with a common denominator that this was a comparison of their savagery with that attributed by Europeans to the Native American tribes of Apaches.
A 1904 issue of the French question-and-answer magazine Intermediary for Researchers and Curious (fr) credited a journalist Victor Moris with the popularization of the term. In November 1900 a police inspector of the Belleville district of police was describing to him a particularly bloody scene and concluded with the words: "C'est un véritable truc d'Apaches!".
A story in a 1910 Sunday supplement of Le Petit Journal claimed that when a certain gang leader nicknamed Terreur (Terror) heard that the actions of the band were compared with these of the Apaches, was so pleased that he proceeded to call his gang "Apaches of Belleville". 
During their heyday, the prospect of being mugged or otherwise assaulted by Apache gangsters was especially feared by members of the emergent bourgeois middle class.
Some of the gangs used a unique type of pistol which was named the "Apache revolver" or "Apache pistol": a pinfire cartridge revolver with no barrel, a set of foldover brass knuckles for a handgrip, and a folding knife mounted right underneath the revolver drum for use as a stabbing weapon.
The Apaches also evolved a semi-codified collection of "tricks" used in mugging and hand-to-hand combat. The most famous was the coup du père François, a tactic by which a victim was stalked by several Apaches before being garroted from behind; one Apache was assigned the job of searching through the victim's pockets for any valuables, while another served as a lookout.
The famous French 10-part 7-hour silent film Les Vampires (1915, re-released on DVD in 2005) is about an Apache gang named "the Vampires". Emilio Ghione's La Mort series of films—of which only I topi grigi (The grey rats, 1918), Anime buie (Dark souls, 1916) and a fragment of Dollari e Fracks (Dollars and dinner jackets, 1919) still exist—was about the adventures of a 'noble' Apache in the Parisian underworld and further afield.
The popular Italian pulp fiction writer Aristide Marino Gianella also wrote a serial novel called Gli apache parigini, which was first available in short installments and then within a complete volume.