The "F3" error code means that the control board senses the oven temperature sensor open.
Remove the oven sensor harness from the control board and measure the sensor resistance. It suppose to be about 1100 ohms at the room temperature.
If the reading is incorrect, replace the oven sensor.
If the reading is correct, replace the oven control board.
- The oven sensor
Part number: WB21T10007 
- The oven control board
Part number: WB27T11252 
Here are the breakdown diagrams and
Replacement parts for General Electric JGS968SH3SS Gas range | AppliancePartsPros.com
Gene.