"北欧日耳曼语系的" can be translated as "Nordic Germanic (in terms of language family/branch)" or more specifically, when referring to the language group, "North Germanic" (since "北欧日耳曼语系" often specifically points to the North Germanic branch of the Germanic languages, which includes languages like Swedish, Danish, Norwegian, etc.).
If you want to emphasize the linguistic family aspect in a broader context, you might say "belonging to the Nordic/North Germanic branch of the Germanic language family".
For a more concise and direct translation in many contexts, "North Germanic" would suffice when specifically talking about the language group.