There are different aspects to consider.
First, in France, even if you're not a taxi, there's a special driving license for "transport de personnes" ("people transportation" ?) which is required if you want to use a vehicle with more than 9 (IIRC) passengers, eg. bus drivers. There's also the matter of insurance. I think we can agree that establishing clear responsibilities and ensuring everyone is properly covered by an insurance in case of an accident is a good thing.
Then there's the taxi license. In France (as in other countries) their number per city is limited. Therefore at the end of their career, taxi drivers sell them and recoup the cost of their acquisition. That's a sum of money they don't want to lose. Those license can get very expensive in major cities like Paris.
Finally there are also some kind of regulations about the car itself (like you have to have a standardized indicator on the roof of the car, a taximeter, etc.)
IMHO we need some reforms to make sure every Uber driver has at least the right insurance and perhaps has followed some kind of course to be able to transport people. As for the taxi licenses, it's kind of an artificially created scarcity. If removed, there are some costs (existing drivers will want to get a refund, then they may want to change occupation, etc.) Finally, as for the car requirements, Uber takes care of the indicator/taximeter. They also have some rules about the cars.
In conclusion, Uber is not trying to disrupt a market, they're going against an existing institution with clear rules and regulations in a lot of countries.