I've read various ways to do it. Do I need to remove my inner fender to replace the fog light bulbs? I can get my hand in there from the engine bay, but I don't know how the bulb attaches inside the lamp so I don't want to break anything.

 

you're never going to get it through the engine bay. take the front wheel off and remove five or six push clips and you'll have all the room you need.

 

This is for an '04 coupe. I noticed your sig pic.

 

That process will work for 04 coupe. Depending on how small your hands/arms are you can get away with just turning the wheels all the way out instead of jacking up the car and taking off the wheel.

 

i owned an 06. believe me, you'll save yourself a lot of grief. if you dont want to take the wheel off, you can turn the wheel. for more room, you can jack up the front (without taking the wheel off). be very careful that it doesn't come off the jack).

 

I simply had the front of my vehicle jacked, you can do one wheel at a time also. When the wheel is off the ground you have more room to remove the clips and 2 screws and peel away the liner. From there if your hands fit you can undo the light and replace without ever having to remove the wheel or liner completely.
It's a bit of a tight squeeze but very doable.