That is (of course) accepted.
It is marking "Nejsem Frantíšek" as wrong for me.
Who would ever say Frantisek nejsem?! My friend speaks Czech 33 years(native) would never say that
I speak Czech for even more years and I would, since I am not František. Perhaps his name is in fact František?
Maybe I'm missing/not understanding something, but Is there a reason why it marks "já nejsem Frantíšek" as wrong?
It is accepted, please do use the "My answer should be accepted" report.
But Nejsem František is correct. František nejsem sounds weird
It is fine.
When would would one say "František nejsem", and when would one say "Nejsem František"?
Both can be used as a reply to someone who thought you were František.
If you just want to announce that you are not František without any context, use Nejsem František! only.