No. Taxis must, by an article of the Code des Transports law added at the end of 2016, accept payment by bank card, whatever the price of the journey.
This came on top of prior legislation which required taxis to be equipped to take such payments but did not oblige them to actually use the equipment.
This is one advantage of taking an official taxi as opposed to a minicab. You can tell a taxi from a minicab, known in French as a VTC (véhicule de tourisme avec chauffeur), because it will usually be identifiable visually and will have a meter.
Only taxis have the right to use designated ranks, for example outside airports, and only they can stop and pick up someone who hails them in the street. VTCs have to arrange beforehand to transport someone, either by phone or internet.
On prices, a key difference is that VTC drivers usually offer a fixed price for a journey, agreed beforehand. Taxi prices are regulated and depend on the number of kilometres covered (or time spent, if the traffic is very slow or the driver has to wait for you) on top of a fixed journey charge.
Taxi fees, both per kilometre and the basic charge, are subject to maximums fixed for the department.
They may be increased in certain circumstances such as late at night, in rush hour, on snowy roads, or going to distant areas far outside the driver’s usual working zone. They mount up on the meter and are not subject to a single fee fixed in advance.
There is also a minimum taxi fee of around €7.