The locals decided it was getting harder and harder to find rats to get paid to capture. They started to cut the tails off and release the rats back into the sewers so that they could procreate.
So the government's attempt to kill all rats ended in rats being bred and eventually an increase in rat population.
Here is one link that tells some of the story:
It seems that the natives were already a lot more enterprising than the French had thought.
I had heard of the story of the Cobra Effect[1] but the Hanoi Rat Masscacre is a much better documented example of the Perverse Incentive phenomenon. It also strikes me as an example of Goodhart's Law[2] in effect.
1. https://en.wikipedia.org/wiki/Perverse_incentive#The_origina...