I've spent a lot of time in third-world countries where most people have no access to regular medical care and certainly not dentistry... and there's no stench of rotting teeth.
There aren't smells of spoiled vegetables or rancid cheese or sour milk -- things are left fresh or composted out back or milk turns to yogurt but it doesn't smell.
People may smell if you're within a few inches of them... but you're usually not. And likewise horses can be smelly when you're right next to them.
But if Paris were really that stench-filled, surely there would be third-world places today that are the same? But I've never encountered anywhere anything like that.
Feels like urban legend to me. Just like the myth about how spices were used to mask the smell of rotten meat. [1]
[1] https://en.wikipedia.org/wiki/List_of_common_misconceptions#...