We're supposed to get one of those spywares any day now, over here in France, thanks to the HADOPI legislation.
When confronted with the problem of making people voluntarily run spyware on FOSS systems, Christine Albanel (ministry of Culture and Communication, proponent of HADOPI), said (my translation):
About software... about free software, of course free software, when you buy, of course, software, for instance the Microsoft pack (this is not free software): Word, Excel, Powerpoint, there are of course firewalls, I just said that, there is security software. But on free software there are also firewalls, which by the way, of course. For instance, we in the ministry, we have a piece of free software, called Open Office and there is indeed security software that prevents the Ministry of Culture to have access, obviously, and the free software editors release firewalls, and even release free [gratis] firewalls. So that argument has no grounds. That is what I wanted to say.
And that is basically the last we heard of it, and they moved on with the project. She said that in front of the entire Assemblée Nationale to the representative who had asked her if she had considered the problem of FOSS systems, including the half-dozen "évidemment" and the unfinished sentences.
Now what happens is that when accused of infringing copyrights, it's the HADOPI authority's word against yours, and despite this being -- supposedly -- a country where you are innocent until proved otherwise, for some reason the burden of proof rests with the infringer here. So your *only* way of demonstrating that you are not guilty is to be running the government-approved spyware, which you can't, because it's HADOPI-style multiplatform, which probably means you can run it on Windows Vista *and* Windows Seven.
Before anyone storms in declaring that's what France gets for being a socialist country and that socialism inevitably leads to governments spying on their citizens: our current government is right wing (on our spectrum), and the Parti Socialiste is against HADOPI.
To conclude, the most likely answer to your question ("What are they going to do? Ban Linux?") is "no, they're just going to pretend it does not exist, and when the time comes to explain why you are not running the spyware, good luck trying to convince them it's related to ethical questions".