They can carry up to 15 people between five stops on a 10-minute route.
The buses, costing £170,000 each, are fitted with high-tech equipment including laser sensors, stereo vision and GPS.
They have already been tested in other French cities and in Sion, Switzerland but without carrying passengers.
The buses are made by Navya and the latest model is called the ARMA.
Navya wrote on its website: ‘The NAVYA ARMA is a 100 per cent electric and autonomous transport vehicle.
‘This innovating and intelligent driverless shuttle can transport up to 15 passengers and safely drive up to 12mph.
‘Entrusted to the best French specialists, its design is the fruit of ten years of research and expertise which allows it to achieve the highest level of autonomy possible: Level 5, making the NAVYA ARMA the first entirely autonomous series vehicle.
‘The NAVYA ARMA calls upon state of the art technologies, developed to ensure safety, comfort and performance.’