Alcohol can actually be protective in a paracetamol overdose. Paracetamol itself isn't relatively dangerous, the metabolic product created by the liver is.
Alcohol use acutely reduces the levels of these enzymes which convert paracetamol into it's toxic byproduct as ethanol preferentially binds to the same enzyme for it's own metabolism. Therefore, acute alcohol consumption can reduce the harmful effects of paracetamol.
The reverse is true for overdose in the context of chronic alcohol use, when the liver adapts to long-term alcohol exposure by increasing the levels of enzymes, therefore rapidly metabolising paracetamol into it's toxic byproduct and worsening harm.
Source: doctor
As a side comment, the lack of medical knowledge displayed in HN threads paired with the absolute confidence some verdicts are delivered with is worrying, and something I thought this forum would be better at than other sites (looking at you, reddit). Paracetamol and NSAIDs (including ibuprofens) are safe drugs if taken to the package directions. Some of the ideas shared in this thread about taking one over the other, or not taking one ever etc, are not rational. Please consult your doctor if you are worried about your particular situation, but generally OTC medicines are not dangerous if taken to the package instructions.
Accidental overdoses of paracetamol are exceeding rare, but intentional ones are common.