How this came about is a textbook case study in government-industrial nepotism, including the family [1] controlling 60% of the taxi companies (edited) literally hiring the head of the French FBI to transfer a couple of months before retirement in the transport ministry, pass anti-Uber legislation, and then retire to a cushy job as the chairman of I think the second or third largest taxi company (owned by the same family). This was exposed in a long article in the Nouvel Obs, a real piece of journalism, which was taken offline about a week after publication (edit - seems to be back! [2]) and before I could take a copy (only the URLs I sent friends remain as testimony of its existence). [1] also claims that the Rousselet family blocked a direct rail link between CDG and central Paris (my Uber on that route last week cost 99 EUR), and has kept the number of taxi licenses "near 1930s levels". edit - [2] claims Paris has 1/5th as many taxis as London or New York, and that no new licenses were given between 1990 and 2002, during which CDG passengers increased almost 50%.
There is an embryonic version of Pool, in the form of Blablacar, an app that arbitrages the very high cost (for French citizen) of SNCF and Air France domestic intercity travel. You post your approximate trip, and riders can ask you to pick them up for a portion of the way. I've travelled 5 hours for 10 EUR this way, and used it frequently between Geneva and Annecy (about 45 minutes, no train link, infrequent buses). Since this app is effectively useless for last minute short trips within a city, it does not compete with taxis, which may explain why it is still around.
[1] Note that the father of the current chairman was the executor of the will of President Francois Mitterrand - https://www.challenges.fr/entreprise/pourquoi-il-est-impossi...
[2] https://tempsreel.nouvelobs.com/economie/20150212.OBS2398/de... - on the former security head: "fin 2007, le gouvernement Fillon demande un rapport sur les taxis au préfet Pierre Chassigneux [...] Coïncidence ? Ancien directeur des Renseignements généraux puis directeur de cabinet de François Mitterrand, l’homme est une vieille connaissance d’André Rousselet via le corps préfectoral. Son travail, publié en avril 2008, est si conservateur que la presse le qualifie de "contre-rapport Attali", qui vient, lui, de prôner une véritable libéralisation du métier. Mieux : ce même Pierre Chassigneux devient ensuite… président des Taxis bleus, poste qu’il occupe encore à ce jour !"