Have a restricted entry for the river - for example, it passes through a hole in the bottom of a wall.

If the river starts to flood, then the hole limits the amount of water that can come through into the city portion of the river, while the wall redirects the flood waters to tributaries or around the city (into a moat?)

The river then exits through a matching hole at the other end of the city, and (optionally) rejoins the overflow.

(The flow rate - or Flux - of water through the hole when it is submerged should be slightly under 14 * Size_of_Hole * Height_of_Water_above_Hole m³s^-1. Build your wall and the flood-plains alongside it accordingly.)

Have a restricted entry for the river - for example, it passes through a hole in the bottom of a wall.

If the river starts to flood, then the hole limits the amount of water that can come through into the city portion of the river, while the wall redirects the flood waters to tributaries or around the city (into a moat?)

The river then exits through a matching hole at the other end of the city, and (optionally) rejoins the overflow.

(The flow rate of water through the hole when it is submerged should be slightly under 14 * Size_of_Hole * Height_of_Water_above_Hole m³s^-1. Build your wall and the flood-plains alongside it accordingly.)

Similarly - if you have a deep /wide ditch or gorge around your city, you have bring the water in via an aqueduct, which will overflow into the gorge in case of a flood, instead of into your city.