I don't agree with a lot about Uber's business model and how it treats its drivers but I have very little or no sympathy for French taxi drivers. This comes from years of running events in France that attracted an international audience. Taxi drivers would regularly massively over charge arriving delegates. For a €70 metered fare they'd insist these unsuspecting foreigners pay fixed fares of between €100-200. That racket was rife for disruption and we were happy when taxi apps appeared and treated customers much more fairly.
and that's only one issue. Paris is the only place where the taxi driver picks the passenger (and not the other way around)... if he doesn't want to go to your destination, he will refuse to pick you up :)
Agreed, this market is ripe for disruption, or at least de-regulation (like giving out more (free) taxi licenses in Paris).