City Bikes vs E-Bikes with baby trailer
First, a city bike is a style of bicycle with sit up and beg styling, generally a single gear or internal gear hub with chainguard (although derailleurs do exist), full fenders, and a step through design. They are also often very solidly built which is a euphemism for heavy. 

An electric assist can be added to any style of bicycle: city, folding, mtb, road, touring, etc. 

So if you like the city bike styling, you should be able to find an electric assist city bike. Or road ebike. Whatever you like. Note that Europe restricts motor output and top speeds, so it's really best to think of it as electric assist. 

Second, you should be able to add a trailer to most electric bikes but you might need the bike shop's help. For example, I have an electric assist folding bike and drag a trailer that is the same design as child trailers and uses the same hub-mounted hookup mechanism. Unfortunately, the rear hub axle of my electric assist is much thicker (12mm) than the hub axle of standard bikes so I had the option of either:


drilling out the trailer mount adapter with a bigger hole so it could fit the larger ebike axle
using an alternate chainstay / seat stay style mount 
using one of the pannier / rack holes  on the rear dropout


I ended up with the third option as it was the easiest. All these should be doable in conversation with your bike shop. Also, since you are likely buying a new child carrier, you have two other options:


Bicycle mounted child seat - either in front of you or behind you
trailer that attaches to the seat stem (thx Willeke)