Turning off the breaker to the oven seemed to reset the oven but not completely.
This would be more consistent with a control board problem.

I like the oven and I'd hate to replace it but it may be more cost effective to do just that.
If you can confirm that it is just a sensor problem, I would take the sensor to a decent sized appliance parts store. They may be able to find a sensor that is close to yours. What is important is how far into the oven, the sensor reaches. You hay have to drill a new hole in the back wall for the mounting screw (not a biggy). Also the if the connector is different just cut the wires off the old one and splice onto the new one. Use the black bakelite type of wire nuts as they are more heat resistant.
Just about all sensors are the same as far as temperature/resistance.

Here are your parts
Replacement parts for JTP10GS JTP11WS models | AppliancePartsPros.com

I looked up F2 and F3 errors for most GE's and it looks like it is related to the temperature sensor/sensing.

I would remove the temperature sensor and check it with a meter, see below.
Also check the the connection to the control board is clean.
If the sensor is OK the control board is probably toast.

Here is a good site
http://www.applianceaid.com/elecrange.html
Check out 7, 8 and 21