All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
If you are confused about the beginning time of Fajr prayer because of the light pollution, or the overlapping of the two twilights -as you mentioned -then do not pray until you become certain that its time has started, or you predominantly believe so; this is very easy, praise be to Allah.
This is because the prayer, whether it is Fajr or other prayers, is not valid unless one is certain or predominantly believes that its time has started. The prayer is not valid while doubting that its time has started. Ibn Qudaamah said:
"If a person doubts that the time of the prayer has started, then he should not pray until he becomes certain that the time has started, or he predominantly believes so. An example for this is a person who has the habit of doing something estimated to last until the time of the prayer, or a reciter (of the Quran) who has the habit of reciting part of the Quran, (and he finishes when the time of the prayer becomes due), and other similar examples. Therefore, if one does so and predominantly believes that the time of the prayer has started, then it is permissible for him to pray. However, it is desirable for one to delay the prayer a little while longer after that, just for precaution, to increase the likelihood of the belief that the time actually started. Nonetheless, if one fears that the time of the prayer will be elapsed, then he should not wait this extra time." [End of quote]
We cannot tell you exactly the prayer times in Cologne or elsewhere. However, you can ask people and they may guide you to a useful site or application to use for this propose.
Allah knows best.