Yes, the hub is identical
Same 5x108 PCD and same 65.1 mm centre bore: wheels from DS DS 4 bolt on and centre on Peugeot 408 without rings. You still need to check the offset and tyres, detailed below.
≈: width estimated from the original tyre size.
Wheel by wheel: offset and tyres
Each original wheel from DS DS 4 is compared with the one from Peugeot 408 of the same diameter: how much closer the wheel gets to the shock absorber or how far it sticks out of the wheel arch, and whether the tyre keeps the same overall diameter.
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≈7Jx17 ET42 · 215/65R17 — Fits like the original
Compared with the original 7Jx17 ET42 on Peugeot 408: shock absorber side 0 mm, wheel arch side 0 mm, tyre diameter +0 %.
Comparison for guidance only (estimated width). Check in detail
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7Jx16 ET29 · 215/60R16
Peugeot 408 has no 16-inch original wheel in our data: check the approved fitments and caliper clearance.
Before fitting the wheels
An identical hub is not enough: offset, width and diameter change the position of the wheel, and larger calipers can touch a smaller wheel. Original wheels often use bolts or nuts with a specific seat: keep the fixings intended for the wheel, with the thread of Peugeot 408 (M12x1.25), tightened to the torque shown on its vehicle page. Finally, check that the size is among the approved fitments for your vehicle. This comparison is for guidance only: have the fitting approved by a professional.
And the other way round: wheels from Peugeot 408 on DS DS 4?