Following on from the recent baguette question (what if the bread kneaders hands were dirty?) French fries cooked in a wire basket in a vat of vegetable oil used only for that purpose. In a diner with non kosher ingredients. Are the main obstacles here: the knife that cut the spuds, and the plate they are served on? If they give me a paper plate... then just the knife? If they tell me it is a single purpose knife. (Or why do I even want to be there? Did not convince the hevre to go to the nearby kosher eaterie.)
The cutting board/counter can also be an issue. If it was used to cut, prior to the cutting the potatoes, unkosher food which is sticky/filmy/greasy etc, that residue can get on to the potatoes. The oil it is fried in would need to be 60 times that unkosher taste. Even if it were, at some point the oil would have gotten enough unkosher taste in it that it no longer could be considered kosher itself See Rema 99:6 so unless the owner changed the oil and your fries were in the first batches that were fried when the oil was able to nullify the unkosher taste, the fries can be unkosher.