Looks like the fog light relay is controlled by the CAN data bus. So, looking at the manual, there are 2 ways of doing this.
First, looks like you can use the output from the foglight switch, and use it to turn on the foglamp relay directly, bypassing the BCM. The relay socket wiring is probably difficult to access though.
Or you could take the foglamp switch output, and run it to your own relay. Then cut and hook the white from the right and light blue from the left fog light to the +12 volt output of the relay.
Now I have not checked this info in my FX, but according to the manual diagrams and my experience, these should work. Unfortunately the manual does not state which wire at the combination switch is the foglight circuit. But they all seem to switch only 6 volts, so that may not be enough to trigger a relay. In that case there is a device called a LVT, or Low Voltage Trigger by Peripheral Electronics that would convert that 6v trigger to a 12 volt trigger.