You need a big can of Barkeeper's Friend (BKF), a sponge with a green scrubbie on one side, and a big barrell of Elbow Grease. The interior of all of the All-Clad Skillets that I know of are lined with Stainless Steel - they do not require seasoning. The black "gunk" you see around the edges is probably grease that has fused to the surface over time from not being properly cleaned after use.
Make a paste of a little water and the BKF and scrub like heck with the green scrubbie. It will take some time - but you should be able to clean most of it off.
If all else fails - you can contact All-Clad via their website
for more suggestions.