Well, both translations are right, but the one you show on the picture is indeed ‘piment‘, the hot peppers — the genus Capsicum (as well as Pimenta). Though, the big ones on that picture, the pepper bells are not piment but ‘poivron‘ (species Capsicum annuum).

The ‘poivre‘ version of pepper is the one that’s usually on the table with the salt (grey or black pepper): the ‘genus Piper‘.

And as a note, the jalapeños peppers (piments) in France is not as widely known as in US or UK, we only differentiate hot peppers by color (piments verts, piments rouges).

“Pepper” has a few different equivalences in French, depending on what you’re referring to. There are basically three different words: poivre, poivron and piment.

Poivre is used to refer to the spice. Therefore black pepper will be poivre noir. Other examples include poivre blanc, poivre moulu, poivre à grain entier, etc.

Poivron is used to refer to sweet peppers. In your picture, it would be the big orange one and the big elongated red one, which would usually be called bell peppers.

Piment is used to refer to hot peppers. They are also often called piments forts. That is also where the adjective pimenté stems from, referring to the hot and spicy flavours.

Depending on the region you’re in, it’s possible that poivron and piment are used interchangeably. In Québec, for example, piment is usually used for most fresh peppers.