SUVs have been hugely popular in recent years in Europe, reaching a record 46% share of new sales in France in May, the same level as traditional sedans.
But Peugeot believes their ubiquity has created a yearning among some drivers for more originality.
"(Some Peugeot 408 customers) wish for a more original and innovating style than a compact SUV, which they deem too common (...)", it said in a statement.
Fastbacks are known for a single slope from the roof to the rear of the vehicle, as seen for example on the Ford Mustang.
So the new 408 is much lower and longer than Peugeot's 3008 SUV, with a flowing and aerodynamic line giving it a distinctive silhouette that sets it apart from mainstream models.
However the new car, which will be built in Mulhouse in eastern France, does have some popular SUV characteristics such as a high ground clearance, big wheels and black plastic covering caps on the fenders, the sides and the rear shield.
The 408 will be launched early next year in Europe and in China by mid-2023, where it will be assembled in Chengdu.
It will initially be equipped with petrol and hybrid petrol-electric engines before switching to a fully electric version.
Check out more information about the new Peugeot 408.