Yes, the hub is identical
Same 4x108 PCD and same 65.1 mm centre bore: wheels from Fiat 600E bolt on and centre on Peugeot e-208 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 Fiat 600E is compared with the one from Peugeot e-208 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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≈7Jx16 ET32 · 215/65R16 — Check on the car
Compared with the original 6.5Jx16 ET32 on Peugeot e-208: shock absorber side +6.3 mm, wheel arch side +6.3 mm, tyre diameter +10.5 % : fit it with the original tyre size of Peugeot e-208 (195/55R16), not that of Fiat 600E.
Comparison for guidance only (estimated width). Check in detail
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 e-208 (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 e-208 on Fiat 600E?