Unfortunately, it is far more complex.
I do not know enough about the U.S. American copyright law to assess whether it’s modeled after that, or not, but: International copyright law (as in: the international law dealing with copyright) is, first and foremost, old. The Berne Convention for the Protection of Literary and Artistic Works was originally signed in 1886. In other words: When Data was thrown back in time to San Francisco of 1893 in TNG 5x26 “Time’s Arrow”, the Convention was already in effect for about five years. I’ll leave it to you to consider whether you’ll find something useful on streaming in that document. It refers to content fixed on media, anyway, so… Well, not gonna help much, this one.
Now, there are definetly some (or some more) bilateral accords on how to deal with copyright. But in principle, every State makes its own rules. Not even within the European Union with its rather comprehensive approach towards harmonisation of legislation (ask the British who are around, they can probably tell you some horrific [and probably made up] story from some campaign involving red busses some years ago) there is a unified approach to copyright law.
How do I know? I happen to live in Germany, that, incidentally, just like France, is part of the EU. Is there something like “fair use” in Germany? Nine Hells, no, there isn’t.
The interesting thing about copyright law is the question who holds jurisdiction. And on this question, courts seem to differ, often claiming jurisdiction for themselves. There’s the case of the Gutenberg project where an American who hosted a work that was under public domain under American copyright law on an American server – who received a takedown order(!) from a German court because the content was accessible within Germany and copyright for the books in question that were published in the 1910s would, in Germany, only expire in 2022 or so.
So, if you would just take Chronic, me, and a Twitch server farm that would happen to be built, just for the sake of argument, in UK, you’d have four possible applicable legislations and possibly even more courts claiming jurisdiction:
- French legislation, because Chronic is located in France
- American legislation, because Twitch is an American company
- British legislation, because the data is actually located on servers in UK
- German legislation, because I access it from Germany
Set aside the fact, that I probably wouldn’t be the only one watching Chronic’s stream.
In conclusion: Copyright law is lower-back-pain, even more so, when you internationalise the case.