I had the same experience. Uber was routinely cheaper than taxis in France. And hailing with an app is astoundingly better than waving at cars in the rain.
There are a few apps that work great in Paris like 'Taxis Bleus' and are more convenient than Uber since you can get a taxi to pick you up in a few minutes (they are usually more taxis around you than Uber cars).
Having said that, I'm all for competing cab services. The French taxi system has been games to protect a the taxi drivers at the expense of the users, resulting in high prices and an less convenience (can't hail a taxi).