Piment de la Jamaïque or poivre de la Jamaïque (Pimenta dioica), is allspice, which in spite of its peppery name is sweet and fragrant, and not spicy hot at all.
It’s also known as tout-épice ou quatre-épices (‘four spices’ because it combines the taste of ginger, cloves, cinnamon and nutmeg).
Confusingly, however, if you buy quatre épices in the shop it will nearly always be a mix of the four spices and not allspice.
Image by Ies on Wikimedia Commons