This is not really about Uber drivers "stealing" customers from taxi cabs. This is about regulation.
The taxi drivers we are talking about are independant workers who paid in the 100k€ - 300k€ range to get a state-regulated taxi licence plate. These plates are resellable, and their number increase very slowly: this means that their price is driven by supply and demand. If new players such as Uber can enter the market, operating under legal loopholes (considered as car sharing and not transportation), the price of the taxi plates will drop because of less demand. This may be good for the customers (increase of the number of cabs, increased competition...) However, you cannot say this is fair for the taxi drivers who took out a lengthly loan to pay for their licence plate - and will not be able to resell them to recover their investment.
So, the way forward for the governement should be pretty clear: either ban Uber, or go for a deregulation of the market. In the latter case, buy back at a fair price the taxi plates from their owners. However at that time, the government has not made a clear choice, which explains the unrest.