Homeless in Paris

Paris has a lot of homeless people and beggars (I'm not sure if they are homeless, or just poor)... more than I have seen in any other city. I pass at least 5 a day. They tend to be mostly in or outside of the metro and there are a few different types:

1) The "typical" homeless man: he's usually scruffy and dirty and sits on the stairs at the metro holding a sign and a plastic cup, sometimes you can find him in his sleeping bag on the sidewalk. Sometimes he has a really cute puppy with him.
2) The beggars who step onto a subway train and launch into a speech about how they need money and then wander around the car until the next stop.
3) The Muslim women that kneel with one arm out, hand cupped, eyes closed. Sometimes they have children with them, I even came across a pregnant woman, and a woman who was in fetal position with her hand cupped on the ground.
4) The mentally ill ones, who sometimes ask for money and other times just rant and make abrupt movements. They can be a bit scary sometimes, and are more likely to harass you.
5) The people who wander around outside carrying a small piece of paper with some sort of written plea on it that they show to anyone who passes by.
6) The ones who come onto the metro cars with a musical instrument, puppets or some other form of entertainment and actually put on a show to try and earn some money.

I feel like I've already become very desensitized to the whole situation and it just seems normal to have so many homeless people around. It's strange that Paris has such a wonderful international reputation and is known as a gorgeous, sophisticated city, yet it has such an obvious dark side. I don't really know much about the issue, but from what I gather it doesn't seem like the city does very much about the problem.