In France a chauffeur service operates as a VTC, a voiture de transport avec chauffeur. The operator is entered on the national VTC register, the driver holds a professional VTC card, and every journey must be booked in advance. A VTC cannot be hailed in the street and cannot wait at a taxi rank. A Parisian taxi can do both, and in exchange it is bound to regulated tariffs.
The two are genuinely different products rather than the same product at different prices, and each wins in different circumstances. A taxi from Charles de Gaulle to central Paris runs on a flat fare fixed by prefectoral order, which is a good deal and hard to beat. A VTC booking gives you a price agreed before you leave home for any journey at all, including the many that fall outside those flat fares, along with a named driver, a chosen vehicle class, child seats fitted before you land and an hour of waiting that costs nothing if your flight is late.