I've shot a bunch of Fox with my .308. Around 2650 FPS with Core Lokt bullets does little damage. We have an overpopulation of Fox around here, I often pop one at the end of my Deer sit. The trick is to wait for your shot and shoot through the lungs, just behind the shoulder. Usually hole in hole out, no expansion. I can imagine 100 Grain .243 shooting below 3000 FPS might get the same results. 2650 FPS, 100 grain, Core Lokt should produce the same results if you want to load your own. Store-bought 100 grn Core Lokt is usually around 2950 FPS.

Gut shooting usually has an explosive effect. Shooting through the lungs is mostly void. but there is always a chance bone or tumbling my make a mess. I've shot a couple head-on and didn't do much damage, lucky I think. I've also made a mess with a couple when they bounded just as I shot and were hit in the guts. Few things smell as nasty as a gutshot Fox, I'm more careful now.

The only way to know for sure is to try it and see the results. I've had the same results with a 7mm Mauser at around 2600 FPS, hole in hole out, with a broadside lung shot.

I even shot a young Fox once (350 yards) with my .308, it wasn't much bigger than a Cat, hole in hole out, broadside, just behind the shoulder.