I don't know why the Minitel failed while the Internet didn't. But the internet started out as a government project, too[1]. Maybe it was because the American government-led effort incorporated the private market better, although, according to your description in the article, the French adopted what was to become Apple's model, and Apple is doing alright so far. And maybe it was due to other reasons, like being ahead of its time, or lack of an international marketing effort (why did the Apple Newton fail?) But in your article you give no compelling evidence to suggest that the Minitel's eventual failure was just a result of it being "state run". Both the internet and the Minitel were state run, and both had a strong private market participation.
If anything, the internet had a very long incubation period in the education system, while the Minitel immediately reached out to businesses. Governments usually don't shine in running businesses, but they do know how to build infrastructure; both the internet and the Minitel are infrastructure, so there's no reason to assume it would fail because it's state-run.
Whatever the reasons, they were more complex than this simplistic explanation (actually, it seems like the main reason is that the internet was already pretty big when Minitel launched – just not in homes – and couldn't be stopped at that stage).
> I think it's still hotly debated and certainly not 'known'.
The measure at which government should regulate the market is debated and varies across countries, but history has proven again and again that neither completely government controlled economies, nor completely free market economies work. We do know that.
[1]: http://en.wikipedia.org/wiki/History_of_the_Internet