Furniture in German is Möbel.
In English, moble is an obsolete word for movable goods, and was spelt mueble or moeble in the 14th-16 c., it is related to the Spanish mueble and Scottish meuble (mobylle, etc.). OED
I don't know when mueblen came to the Netherlands, but more likely it came from Germany. Scotland had many Dutch workmen and artisans in the 15th-16th c, and adopted some of their styles in building and furnishings so perhaps they picked up the word from the Dutch.

However, how all this came about, I dunno; I would be guessing.