I see this sort of shit all the time, usually from homeless people.
Once I was walking past a fountain in the 9e arrondissement and I saw two homeless guys start fucking in broad daylight. Literally pants-down, dick-in-ass action at 3 in the afternoon in front of a marble 18th century statue.
A few months ago, I was walking along the rue St-Denis (the main prostitute district) at night when I saw a humongously fat black woman storm out of a building, wagging her finger and rolling her eyes. Then some skinny old dude with no shirt came out after her and started pleading, "please baby, I need you, I'm so in love with you!" to which she replied, "you ain't no good, you ain't got no money, I ain't fallin' for that one again!" It was pretty hilarious.
Paris has a ton of batshit crazies who scream at the top of their lungs or who talk to themselves constantly. It's so common that I don't even really notice it anymore. There are also tons of guys who piss on the sides of buildings.
The staircase of the Bastille opera is home to a motley collection of scum and riff-raff who haven't bathed for days, spend all their time drinking shitty lager and all seem to own massive rottweilers which they keep on chains. They all have dreadlocks, dress in black or in military fatigues, and smoke used cigarette butts found on the ground. The other day I saw one of them had brought her baby in a carriage while the rest were milling about drunkenly. Another time, I watched as the alpha male of the group had found some french fries in a dumpster and took pleasure in feeding them to his dog while some other dude groveled at his feet to ask for a taste.
Honourable mention to the crazy homeless lady near my office who has constructed some sort of nest in the lee of a building and holds up a sign which reads, "please ask M. xxxx why he ruined my directorial career and forced me to live on the street" followed by a phone number. Sometimes she screams at you if you stare at her too long.