It's actually spelt Soufriere. Soufriere doesn't smell bad at all. Occasionally you may take the smell of the sulphur springs in the town of soufriere but that in my mind is not a bad smell. I actually like the smell. I think that the smell is good for you (according to the scientists). If you go to the sulphur springs/volcano itself, then you'd take a stronger smell of the sulphur.
To me it's all about perspective. Largely, soufriere's inhabitants don't spend any time worrying about the smell of the sulphur springs or think of it as a bad smell. It's a non-issue. I can tell you this having lived in Soufriere. There's nothing to be concerned about.
Soufriere is called soufriere because of the presence of the sulphur springs.