Sorry to ruin your fun but in German it's actually just Bürger (capitalized because all nouns are). Though the true etymology might be entirely different.

Bourgeoisie or Burgher in English, Bourgeois in French or in German Bürger, all from old Frankish burg, for town. English has both words, but they now have different meanings, and the term Burgher is mostly obsolete.

The divide (or perception of a divide) between city dwellers and the country is not something the US invented, these divisions predate the colonisation of America.