That being said, in general, the state is a passive investor. What happened with Dailymotion is way different.
First, the issue came from Arnaud Montebourg, a powerful Minister of the Economy with statist views in the former Socialist government. The current government is very different. (By the way, Montebourg was replaced by Emmanuel Macron, the current President of France, as Minister of the Economy under Hollande.)
Second and most important, by the time this happened Dailymotion had already been sold. It was a wholly owned subsidiary of France Télécom, the largest telecommunications operator in France (commercially known as Orange). That operator was state-owned until 2004, and even today the State is its largest shareholder.
In other words, the State prevented a former public company it basically still controlled from selling a wholly-owned subsidiary which happened to be a startup it bought before. I disagreed with the decision then, and I still disagree today, but it didn't prevent an exit. Rather, the actual exit of Dailymotion was to a company owned in part by the State...
EDITS:
- Looks like I was too slow to post and senko beat me to it.
- The "FSI" articles linked by others talk about, which invested in Dailymotion, is now part of the "BPI" I mentioned (it was merged with other vehicles that invested at different stages).
- Some French people regret Montebourg style, for instance a journalist recently tweeted his disagreement about the governmental OK to the sale of Photonis, a night vision company, to a foreign group (https://twitter.com/VincentLamigeon/status/11742379454543708...).