The issue here is the neurotransmitter serotonin. Paxil and other SSRI (Selective Serotonin Reuptake Inhibitor) drugs work by preventing the brain from breaking down serotonin, which results in an increased level of serotonin in the brain tissues.
Drugs like cocaine (and to a lesser extent alcohol) work in part by changing the chemistry of serotonin receptors in the brain, causing a buildup of serotonin in the tissues.
The problem is that these two drugs work in different ways, and as a result the combination can drive serotonin levels up extremely far, which can have disastrous consequences. These complications can include seizures and elevated heart rate; a serotonin spike is considered to be a medical emergency that can be fatal is left untreated.