As the OP mentioned, that style of pan is called a French Skillet. It's kind of a hybrid between traditional saute and fry pans, and not as deep as a saucier. Also note that there is no flared lip.
Although it isn't exactly the same as the one used in the video, All-Clad makes a similar model. Personally I wouldn't pay this much money for a non-stick pan, but here's a link if you're interested:
All-Clad Tri-Ply Stainless-Steel Nonstick French Skillet | Williams-Sonoma