If I build a extension in my Software which opens Google Maps in the default browser with the Address of a Contact, do I need a Licence and start a plan at Google?
Like: https://www.google.de/maps/search/Kongo+Kinshasa
On some Pages I found, was mentioned that the use of Google Maps Urls are free, but I'm not sure.
There's no need to start a plan or acquire a licence from Google to be able to use the Maps URLs.
You just have to observe Google Maps Platform's Terms of Service in implementing this service in your use case as Google Maps URLs are also bound by these terms.
And lastly, you are correct to say that Maps URLs are free of charge. You won't even need an API key to use it.