I recently discovered that the words poison and poisson, meaning poison and fish in English are very similar, despite not being contextually even close. Might it be that fish might rot and become poisonous? I haven't found anything that might even suggest an answer.
I would say this is accidental.
The word 'poisson' comes from the Latin piscem, meaning fish, while 'poison' comes from 'potion' which itself originates from potio, also Latin but meaning beverage.