How big are the berries? Have you looked @ S. nigrum?

https://garden.org/plants/view/92859/Black-Nightshade-Solanum-nigrum/

The berries are the size of black currant.

It probably is Solanum nigrum. That species is the most abundant in your area. There is a lot of variation in this species. The leaves can be lobed or unlobed. I guess you can say the 'lobes' are blunt serrations. There are many varieties, subspecies. It is now usually called the Solanum nigrum complex. The photos aren't crisp enough to see small details or pubescence, so if you think it's something else, only you are close enough to make comparisons.