Knowledge-based skills would certainly be impaired, or lost completely. The rest is up to you, I guess.
Speaking purely from my own experience, and not any wider medical knowledge of the different forms amnesia can take, I would tend to agree with Wednesday Boy but not to fully agree with LightningArrow.I think it would be more interesting to allow the abducted character to retain knowledge of their home world and explore how they would react to differences in the worlds. For example a character abducted from Dark Sun might have a fear of FR halflings because they're used to Athas' cannibalistic halflings. Or a dwarf abducted from Dragonlance might be surprised to be welcomed as one of Bruenor's kin when they're a lowly gully dwarf.
As I posted upthread, even when, due to prospective amnesia, I was "resetting" every 5 minutes or so, and due to retrospective amnesia had lost about 3 years worth of personal memories, I still had my professional knowledge. So I think an amnesiac's knowledge skills should still probably work OK. That said, there may be issues if you're wanting to run a FR game and don't want the PC to be making knowledge checks about GH, Eberron or whatever. Maybe discourage the player from taking training in History and perhaps even Religion (but Arcana, Planer Knowledge etc might still be OK as that stuff is a bit more generic and remains valid across worlds).
On Wednesday Boy's comment: I think the amnesiac is still going to have a general sense of the social world. For instance, when I had amnesia I still knew about paramedics, doctors, nurses, hospitals, etc. So if the social world the amnesiac character finds him-/herself in differs from the one s/he is used to (eg dwarves are honoured rather than downtrodden), that should come as a surprise.
Again, you'll have the issue of balancing that sort of thing which might be fun against a wholesale importation of knowledge of another campaign world, which you might want to block if you're trying to focus the game mostly on FR.