German troops crossed through Belgium in an attempt to flank the French forces lined in trenches along the border.

troops = Truppen

German invasion of Belgium, Netherlands, and Luxembourg.

No. Even as they paraded in Paris, German troops did not pass through the Arc de Triomphe, because of the Tomb of the Unknown Soldier. The idea that they marched through comes from the pictures of German troops coming down the Champs-Elysees avenue with the Arc in the background. But on the Etoile square, archives clearly show that German troops went round the arc, using the regular road. German officers equally agreed to the daily ceremony at the tomb, allowing French veterans from WWI to rekindle the Eternal Flame on every day of WWII.

The nameBrenda is also used in Germany. It comes from Scandinavia.