"Je les tousserai" means "I will cough them".

How you interpret it is up to you. Ultimately those are song lyrics so it’s an art piece and interpretation is personal.

The first question would be: what does the pronoun "them" refers to? Because earlier in the paragraph, there is a mention of "leur émeute" (their riot), the pronoun is referring to the same subject: the persons rioting.

When you read the full lyrics you realize that the line was written in order to rhyme with an earlier line "Je les pousserai sans qu’ils s’en doutent".

My guess is, the author was looking for a rhyme. There’s no true meaning to the sentence (one doesn’t actually "cough" someone else) so again, the interpretation or the poetic meaning is left to you.

Tousser is indeed an intransitive verb, so this is a case of "poetic licence".

If we accept that it is used here as part of a metaphor, here is my interpretation: tousser, just like to cough, means to expel air out of your lungs, usually to expel something supposedly bad for your body (germs, fluids, foreign particles, etc). Metaphorically, Paris (or France, or society at large) is the body, and rioters are like germs: Javert wants to expel them and get rid of them.

I learned something today…

If you refer to the french Wiktionary entry for tousser, you’ll notice the usual intransitive meaning (to cough), but also a second, "rare", transitive meaning:

Tousser quelqu’un : manifester, par un toussotement, de la désapprobation à ce qu’il dit ou à ce qu’il fait.

Which means disapprove the words or acts of someone by coughing. The example is of course from Victor Hugo, which is quite fitting here.

Note that in the common language, there are actually transitive forms of tousser where the object is what is being coughed (blood, most often: tousser du sang).