Are you asking why they kept the Dutch colors but ditched the Dutch lions? ;)

The lily (fleur-de-lis is the stylized/heraldic form) ties the city to its Merovingian-Carolingian roots. With the creation of a French national mythos in the Middle Ages came a bunch of legendary variants relating (Merovingian king) Clovis I to the fleur-de-lis, and by the late Middle ages the (French) fleur-de-lis and (German) eagle were seen as the joint emblems of Charlemagne. Historic Wiesbaden was very proud of its Holy Roman Imperial roots: it hosted one of the royal palaces in the peripatetic 8th-9th centuries.

In the high Middle Ages (13th century, I think?) the city fell under the purview of the Count of Nassau (this is distinct from the independent Duchy of Nassau it would join in the 19th century). Nassau's colors are blue and gold; the coat of arms resembles the Dutch lion. That's where Wiesbaden gets the blue and gold.

For a period of time around the turn of the (ETA 20th) century, the city used both the fleur-de-lis and the lion in its coat of arms.

I'm not sure why they ultimately dropped the lion or why there are three lilies, but overall, that's why a German city uses French symbols and Dutch colors.

This is more a point of historical curiosity than an actual answer, for reasons I'll get to. /u/sunagainstgold covered the actual answer, this is really just an aside.

Wiesbaden was the capital the Duchy of Nassau until 1866, when, for punishment for backing Austria in the Austro-Prussian War, the Duchy was dissolved and subsumed into the Kingdom of Prussia as the Duke had allied himself with Austria.

24 years after the Adolphe was deposed as the last Duke of Nassau, he inherited the Grand Duchy of Luxembourg after the death of William III, his 17th cousin once removed (this is the greatest genealogical distance of sovereign succession in history, I believe), due to a rather complicated set of succession laws and a family pact. Adolphe's great-great grandson, Henri, is the reigning Grand Duke. Today, you can still see the same three golden fleur-de-lys in the center of the Grand Duke's personal arms as are seen on the coat of arms of Wiesbaden and the Grand Duke of Luxembourg continues to use Duke of Nassau as part of his full style.

BUT...

The two have nothing to do with one another. It's really just an interesting coincidence. The three golden flour-de-lys in the Grand Duke's personal coat of arms represents the House of Bourbon-Parma, which only fell to the family of the Grand Duke in 1964.