Paris doesn't take a bad photograph. Ditto the Côte d'Azur, the fields of Provence and the Dordogne. France may be the most camera-ready country on the planet. Economically, however, the French picture is a bit bleaker. Unemployment is up, manufacturing output is down, and the eurozone's second-largest economy is labouring under its second-worst industrial sector.

And yet, this week's dour news seems hard to swallow upon laying eyes on the scintillating Peugeot Fractal, previewed ahead of an official unveiling later this month at the Frankfurt motor show. This one-off design study does not necessarily presage a specific Peugeot model, but rather exists as a way of reminding the world that the lights are still on at 75 Avenue de la Grande Armée. This two-plus-two coupe-cabrio has the proportions of a two-seat sports car, with a long nose, a short deck and the slightest fore and aft overhangs. The car is shorter end to end than a 208 supermini, and its shape — particularly the chiseled front end – offers a squinting glimpse of future Peugeot familial features.

The French automaker calls the Fractal an Urban Electric Coupé. It takes its motivation from a pair of small electric motors, one at each axle, producing a combined 201 horsepower – modest, but sufficient. The Fractal's wheels, similar to those on the BMW i3, are broad – 19 inches in diameter – but narrow, and wrapped in low-rolling resistance tires to help maximise battery life.

Naturally, the Fractal is a concept car — and a French concept car — so there's plenty of whimsy in the design and equipage, most of it related to the car's audio system and all of it designed to capture the imagination of millennial buyers. The interior surfaces, including the floor and door panels, are covered in 3D-printed acoustic panels like you'd find in a sound-absorbing anechoic chamber. The surfaces are intended to improve clarity and response from the stereo’s 12 speakers, sourced from France’s high-end audio equipment maker Focal. The setup, which was designed with the assistance of Brazilian electronic music composer and producer Amon Tobin — the artist formerly known as Cujo – features a SubPac tactile bass system, which uses vibrating "speakers" in the seat backs to send low-frequency pulses directly into occupants' spinal columns. Tingly.

Exterior lighting is nothing short of dazzling, with turn indicators that mimic the lights on a recording studio graphic equaliser and cool blue LED heartbeat lights that pulse while the battery is charging. A holographic digital display dominates the Fractal's dashboard behind a raft of thumb switches and an oval steering wheel with two tiny integrated touchscreen displays. And the car whirrs and hums in futuristic ways (also created by Tobin) to alert pedestrians to its presence (This last bit is no wild imagining; all EVs will soon be required to produce below 30kph, per European Union legislation.)

There is little question that elements of the Fractal will appear in other Peugeot models in the coming years, but it's a pity that the car itself isn't directly production-bound. But that's the mark of a great concept car, really: one that is not merely packed with great ideas, but one that is a great idea. The Fractal succeeds at a none-too-easy task: it manages to inspire optimism for the future of Peugeot, and for the future of France.

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