As mine was.
Here's my tuppence worth feel free to disagree...
Fiat 500's and many other vehicles, have an IC embedded on the negative battery terminal, known as an Intelligent Battery Sensor (IBS), whose purpose is to lower emissions, and determine the batterys' ability to provide the start/stop service as well as many other things. Normally a single wire plug to the (also smart) alternator on a communication protocol called LIN.
IMO The IBS has failed If;
A. The charging system in not charging, and you have no dash panel warning light.
B. You have a newish battery with CCA in excess of 460A the higher this figure better, (but it must fit in the available space) & preferably AGM technology.
C. You have proven that both engine earth cables are at zero resistance, not by measuring with a digital multimeter. But by physically cleaning and/or replacing them.
D. When you unplug the IBS cable from the sensor and the battery charges at between ~13.1V & ~14.2V depending on load.
If when you unconnect the sensor cable you blip the throttle the alternator will self excite and the internal voltage regulator will control the charge as the old system used to do (assuming that the voltage regulator hasn't failed too). This also proves that your alternator is ok.