Depending on the motor you may not do damage to it if the motor was able to keep rotating for some time.
There is a solution to your problem and it is to add a low voltage relay if the Float switch does not work --
Also, you could use 2 float switches placed in series if one is stuck the other will operate.
Can you tell us what is the current of the pump motor, I may presume that is a brush motor type.
To be able to guess if you may have a winding problem due to the stuck float switch, please say the shallowness of the well and the total head that the pump operates on, from the well to the reservoir.
The ideal relay should be a step relay to save power -- a pulse for ON and another for OFF.
The best circuit is one that the float switch energizes and once it reads low voltage triggers the OFF pulse.
Let me know
Nando