2013 Fusion both low beam headlights suddenly stopped working

Check the bulbs first, two blowing at the same time is uncommon but not unheard of (think about it, when one is on, Sonos the other one, life expectancy won’t be much different) I like the K.I.S.S. diagnosis method the best. If they’re good then check low beam fuse and relay (I would swap it temporarily with the high beam relay because you know they work, if the problem follows the part, the problem IS the part.). If those don’t identify the problem then I would check the switch last.

Check the SJB (Smart junction box) to make sure its outputting the signal like it should. I repair many ford sjb's for lighting issues. The 13 fusion I'm not to familiar with but the previous generation had big problems. I actually have a 13 edge sjb on my bench right now to be repaired for dead low beam drivers. You are probably in the same boat if they both went out at same time.