Translation:There are not many fish in the rivers, from which the German airplanes take off.
German planes take off from the rivers? That doesn't make sense and it made me doubt whether my translation was correct (but it was).
There are water airplanes that land on and take off from bodies of water. Usually lakes, but there's nothing speaking against taking off from a slow-flowing river either.
Why is this not accepted: In those rivers are not many fishes, from which the German airplanes are taking off. I started many times from German airports, but luckily always from the rolling field and never from rivers.
I would say it is about the first part: it's better to say "there are not many things in that place." or "in that place there are not many things" than what you wrote "in that place are not many things" it's about the "there are..." phrase.
Also, the plural of fish is a bit weird. it is usually "one fish, many fish", except if you want to express multiple species of fish in a biological context, then you use "fishes". So, "There are many fishes in the lake" doesn't mean that there is a large number of fish in there, but that there is a large variety of different fish species. I'm not sure whether that should be a reason for rejecting the sentence, though. English native speakers should judge how grave a mistake that really is.
Another reason could be the ing form, which you used in the second part, but that should definitely be accepted.
Is this a natural sounding phrasing in Hungarian? It certainly is not in English.