"Finders keepers" is a legal principle only common in common law countries. In most of the world, in no way could you be construed to own something just because you found it in the ground.

In most civil law countries, everything always has a legal owner (usually reverting to the state when no other legal owner can be found), and if you just "find" something and take it, you have committed theft. In Germany, the antiquities law is clear that anything of significant historical value belongs to the state, with a monetary reward possible for the finder in some situations (and finding something and not reporting it is a crime). If an old coin is deemed to not be historically significant, it probably belongs to the landowner.