"Free market" is not really a reality in France; it's not just "second to politics", it is hated for its own sake. Competition is considered a bad thing; the reasoning is that it leads to waste, that resources are better allocated when centrally planed by civil servants who don't have a dog in the race. Many sectors in France still operate exactly like that, in 2014 -- not just taxis; for example if you want to sell cigarettes you have to apply for a licence to the state and you'll only get it if you're far away enough from other cigarette sellers.
It must sound crazy to non-French people but that's just the way it is; is it sub-optimal? Yes. Stupid? Probably. Will it ever change? I wouldn't hold my breath. This is how this country is and thinks.
But, in the case of the taxis, they have a reason to be upset; they all buy their licence for a very expensive price (I believe half a million Euros), usually borrow the money for it and have to somehow pay it back. If they are suddenly out of business or their licence worth nothing, it's a problem.
In order to free this market, the problem of the licence has to be addressed (state buy-back?); or, maybe, the govt. can decide you don't need a licence anymore: taxis will be extremely upset for a while, and then when the dust settles the problem is solved.
In typical French fashion however, the current govt. has decided nothing; non-taxi taxis can operate with a stupid 15 minutes delay, which is supposed to appease the incumbents.
This 15 minutes delay is even worse than it sounds, because it doesn't apply to 4- and 5-star hotels!! (And this is a leftist government). If you want to call Uber from the desk of the George-V you don't have to wait; if however you're calling from Hotel Ibis in Pantin then you do have to wait.
Go figure.