Admittedly it has been a while since I've been in Paris but as far as I know the city does not have an above average problem with homelessness or mental health, particularly in its metro system. I know it's a huge problem in the U.S., though, so maybe you are confusing the two contexts.

Paris also has a substantial bus system and the article highlights the opportunities created for biking. So even if the metro would have problems, many people can rely on other modes of transport.