If a gentile cooks a baked potato is that bishul akum? what about if the gentile slices the potata into french fries? Are these items considered to be served at kings tables?
A baked potato would fall under the prohibition of bishul akum, as would french fries.
Sources: Aruch Hashulchan (113:8) writes that potatoes are food of the poor, and that they are not served at kings’ tables, explaining that authorities who prohibited potatoes (Chochmas Adam 66) must have referred to a place with different royal table manners. Today, potatoes (in various forms) are served even at “important” or royal meals (as a side dish), as are even french fries, and the prohibition of bishul akum would apply to them.