If you think about a small French car you probably have something cheap and cheerful in mind. DS wants to change that thinking.

It has the ambition to become a leader in the premium SUV segment and wants to achieve it with a range of luxury, electrified crossovers.

The new DS 3 Crossback is the brand’s latest model and comes complete with a fully-electric version.

It is neatly styled and demonstrates a flexible new platform from the PSA Group, which will eventually underpin most of the company’s new models – including the new Peugeot 208.

The 3 Crossback is about the same size as most small crossovers. Think Kia Stonic, Renault Captur or Seat Arona. But, DS says it is a premium model and, therefore, a rival for the Audi Q2 and Mini Countryman. This means you can spend more than £35,000 on a small French crossover, with a three-cylinder engine!

Fleet customers are likely to opt for the entry-level Elegance model, priced from a more realistic £21,305. Prices for the electric version are yet to be announced.

While it doesn’t look particularly impressive on paper, the DS 3 Crossback does feel a bit more special than the usual crop of mainstream models.

The powertrain line-up consists of 100PS, 130PS and 155PS versions of a 1.2-litre petrol engine, a 100PS 1.5-litre diesel and the electric E-Tense.

The petrol models are expected to be the most popular, emitting from 113g/km of CO2.

In the E-Tense, the 50kWh battery can provide up to 180 miles of range and it offers 136PS.

We only drove the electric model for a few miles, as it is still, technically, a prototype. What impressed us is how it is indistinguishable from a petrol or diesel model. 

The petrol engines do a decent job of hauling the 3 Crossback around in relative refinement and complement its chassis, providing a smooth ride.

Body roll is minimal, with responsive steering making the car feel nimble and light. Despite the firmer suspension setup, ride comfort is excellent.

The interior won’t be to all tastes, but it certainly reflects the brand’s luxury aspirations. The high-spec ‘La Premiere’ launch models have a leather-clad dashboard, matrix LED headlights and a Focal audio system.

All versions get electrically retractable door handles and digital instruments. Sat-nav only comes on Prestige models (from £24,950) and above, though. To get heated seats, you have to opt for the range-topping Ultra Prestige, which starts at more than £30,000.

Interior space is limited as the car is relatively small. The boot is one of the smallest in the segment; at 350 litres it is 100 litres behind the Countryman.

DS doesn’t talk about volumes, but we don’t expect the 3 Crossback to be a huge fleet seller. It’s decent enough, but, in reality, a VW Golf makes a lot more sense for those who want a practical, efficient and premium-feeling hatchback.