More than 60% of the US and world music market go to UMG, SonyBMG and EMI. Who owns them? UMG is French, Sony BMG is Japanese (it used to be Japanese and German), and EMI is British. Yes, Hollywood and the US music industries pushes restrictive copyright legislation. So do European publishers, directors, writers, and artists, as well as European governments who like to make their media happy. And the legal situation surrounding copyright and fair use is restrictive in Europe already, and has always been.
The DMCA wasn't something invented out of thin air by the US, it was the implementation of a WIPO agreement. Europe implemented the WIPO agreement with a number of directives, including Directive 2001/29/EC, which in some ways is more restrictive than the DMCA. But Europeans don't follow EU politics much; to them, it looks like the US implements some draconian law and then Europe is made to follow, when in fact, the real reason is that both EU and US special interests perform policy laundering at WIPO, and the US just happens to be a bit quicker implementing it.
If you're a geek interested in keeping fair use alive, the "blame the US" approach isn't going to work because the US isn't the primary source of the problem. The problem is media companies. European media companies have much tighter control over European public opinion and politicians, and they love to present these issues as "evil American companies like Google want to steal European culture and impoverish European artists" and at the same time "the evil American government is forcing our poor politicians to implement all these draconian laws that we don't really want to implement but are bullied into". Stop letting yourself be manipulated and get the facts. These laws are going to keep coming until the politics in countries like France, Germany, the UK, and Japan change radically.