I recently read an article accusing someone of pedalling false hope. I don’t think it’s possible to pedal false hope.
You can pedal a bicycle, but that’s about all. You could, however, peddle false hope. Peddle means to try to sell [something, especially small goods] by going from place to place. Or, figuratively, to promote [an idea or view] persistently or widely.
If you peddled an idea that was later found out to be bogus, you might have to backpedal.
You can read about the difference between peddle and pedal and a whole lot more, in the Clifford & Co editorial style guide.