I am going to be living alone in Paris for 6 months for an internship. As far as I know, I don't know anybody who lives there or is gonna be there at the same time. I am a relatively introverted person, so I am a bit nervous about making friends. I am a 19 year old american, and my job will mostly be with people considerably older than me, though maybe a couple interns will be in my age range. I am a jazz musician (pianist), I love art, politics and philosophy, and though I am introverted, I am down for most stuff. If any of you have suggestions for me to make friends, that would be incredibly helpful. It would be even more helpful if you had advice specific to my interests and provided specific sites that could help me. My French is fluent and should show no hinderance. I can also speak Spanish fluently (if that has any effect on answers).
Given that you're a jazz pianist, one fun (and Paris-specific) way to make friends could be to play one of the many pianos available in public places. Those would be, e.g., all major train stations and some malls (Les Halles has one). There's always people listening and appreciating your music, often chatting you up after you stop playing. There's people playing regularly, too, so maybe you can get in touch with them and improvise together etc.
I, too, am an introvert, and when I was younger, I moved to the US whilst knowing nearly no-one there. I play trombone, so I took my instrument, and pretty much the first thing I did was find ensembles to play in. 25 years later, most of the friends from that time that I'm still in touch with are the ones I made in those ensembles (plus you heroic NEDoDders, if you're reading this).
Everything you need, you already have: you can speak the language, and you play an instrument. Go to Paris, and make music; it is almost impossible that you will fail to make friends while so doing.
In terms of finding someone to play with, my little sister (until fairly recently a musician in Paris) recommended searching Facebook. While I won't use Facebook for any reason at all, she said that a very small amount of searching turned up the "Paris Jazz Jam Sessions" group, which looked promising to her.
You could try meeting people through Meetup, for example there are lots of music-related Meetup groups in Paris but there will also be others related to art, politics and philosophy.