The common crossword answer for “unfounded rumor” is CANARD (6 letters).

Other possibilities you might see in crossword grids, depending on letter count and crossings, include:

  • MYTH
  • IDLE (as in “idle rumor”)
  • RUMOR itself in some clue/answer rewordings

But if your clue is exactly “Unfounded rumor” and needs a 6-letter answer, CANARD is almost certainly what the puzzle wants.