Sarcasmes translates to "sarcasm" or "sarcastic remarks". It's a less common word in everyday French songs, making it stand out.
In this song, Serge Gainsbourg uses it to describe the hurtful words directed at him by Marilou, which are the "premières atteintes du mal" (first signs of illness) he experiences. The word perfectly captures the biting and critical nature of the insults, setting the tone for his subsequent physical and mental decline.
This is the moment the narrator notices he is coming apart. Marilou keeps mocking him, and her words land hard enough that he feels them physically. He says his ears turned into cabbage leaves after being called an old fool, which is his way of admitting the insults left a mark he cannot hide.
The rest of the song follows one wrecked morning. At first light he stocks up on cigarettes at the tobacco cafe, asks for a full tank of fuel at the counter, then drags himself into the toilets to throw up the drink and the anger together. On the way home the children laugh at him.
The last line ties it up: little by little he has taken on the face of a boxer. Cauliflower ears and a beaten-up face are what you get from taking hit after hit, and here the hits are words from someone he loves. It is Gainsbourg writing about jealousy and humiliation as if they were injuries, which is why the song is called first symptoms rather than anything more dramatic.