I think the best English equivalent for it is urchin, as in a street urchin. Bear in mind that the quintessential titi parisien is Victor Hugo’s Gavroche.

In Dictionnaire des locutions françaises, un titi (pop.) is given the following grammatical explanation:

Le mot est sans doute de formation enfantine, un redoublement de
[pe]tit.

According to the TLF dictionary, le titi parisien is a ‘typical’ parisian kid. Like Gavroche, as Indoxica said in his answer, un gavroche being a synonym of un titi parisien according to the same dictionary.

This kid doesn’t exist anymore though. This expression refers to kids of the mid/late 19th century.

That’s what wikipedia says about the expression, but actually what we call “titi parisien” is also the patois/local dialect that used to be talked in 1920-30 in Paris with expressions like “meszigues/teszigues/seszigues” as to say “moi/toi/lui”. But that’s a parisian thing (aa)

As a French, please allow me to answer your question, backing up on the French wikipedia that seems complete.

Titi parisien est une expression familière, en France, pour désigner un « enfant de Paris », déluré, dégourdi et farceur, dont l’archétype est le personnage de Gavroche dans le roman Les Misérables de Victor Hugo ; puis, par extension, un adulte issu des classes populaires parisiennes.

A “Titi parisien” is a colloquial expression, in France to define a “child of Paris”, resourceful, bright, and a practical joker, the archetype of which is the Gavroche character in “les Misérables” by Victor Hugo; then, consequently, an adult from popular classes in Paris.

You may Google “Titi parisien” and look at the pictures. All those with a cap on represent the titi parisien I grew up knowing.