I would expect that a non spinning pump motor would trip a breaker before a GFCI as well. Here's a little more detail on how they work:
A residual-current device (RCD), or residual-current circuit breaker (RCCB), is an electrical wiring device that disconnects a circuit whenever it detects that the electric current is not balanced between the energized conductor and the return neutral conductor. Ground Fault Condition is defined as: An unintentional, electrically conducting connection between an ungrounded conductor of an electrical circuit and the normally non-current-carrying conductors, metallic enclosures, metallic raceways, metallic equipment or earth. Such an imbalance may indicate current leakage through the body of a person who is grounded and accidentally touching the energized part of the circuit. A lethal shock can result from these conditions. RCCBs are designed to disconnect quickly enough to prevent injury caused by such shocks. They are not intended to provide protection against overcurrent (overload) or short-circuit conditions.
More information: https://en.wikipedia.org/wiki/GFCI

Basically, if your GFCI is tripping you have a potentially hazardous situation. Is there any corrosion on the pump motor or wiring? If you can remove the back cover where the starter is, do you see any corrosion? If so, you might need to replace the pump. You can check the impeller to see if it freely turns, it won't hurt.

Also, inspect your earth ground and bonding lines. If you're grounded but not bonded, it could lead to current leaks across circuits which should trip a GFCI.