If you specifically want an auto I'd look at the 500x instead. The 500L uses the older and sometimes very problematic Dualogic auto gearbox, which is only fitted to the 1.3 Multijet 85bhp diesel. The engine is fine but it might feel slow after the 180bhp Peugeot. Whereas the 500x uses the newer DDCT/DCT (dual-clutch transmission) which has proved much more reliable in the Alfa Romeo MiTo and Giulietta that it's been fitted to since about 2011. You'll mostly find it fitted to the 1.4 MultiAir 140bhp petrol, but it may also have been available with the 1.6 Multijet 120bhp diesel for a time (it was in other Fiat Group cars).
The 500x also has a more traditional auto gearbox (7 speed) fitted to the 2.0 Multijet diesel models - not perfect but it's a world better than the Dualogic, which I'm afraid to say is neither reliable or particularly pleasant to use.