This is a rare scenario but we have seen it. This is caused by the grounding function of the fog light assembly being tied to the high beam system. You will need to install an inline resistor with your fog lights to reduce the electric load. If that does not work then try grounding the ground wire itself to the frame of the truck.
You can also try the 'Bambi' mod which resolves this issue. (an issue caused by the fog units and high beams being on the same 'circuit.'
Below is an example of the bambi mod being performed, posted by a fellow F150 owner.