Even where it happens (it's common, the cases I know personally are Nantes or Antwerp) it's still obvious which side is right and which side is left, it's simply according to the main flow of the river.

Although in this instance, I think it's more common to talk about north/island/south in Nantes rather than left/right banks. While Antwerp's part on the left bank is literally called "left bank" (Linkeroever).