"北欧日耳曼语系的" can be translated as "of the North Germanic (language) family/branch" or "pertaining to the North Germanic linguistic group" in English.
If you are specifically referring to languages within this family, you might say something like "the North Germanic languages" (e.g., Swedish, Danish, Norwegian, Icelandic, and Faroese).
For a more concise adjectival form in a sentence, you could use "North Germanic" to describe something related to this language family, such as "North Germanic languages" or "North Germanic linguistic features."