The Torah says (Deuteronomy 22:1): "Do not see your brother's ox or ram straying on the road and ignore them; you must return them.""
The Torah commands that lost items found by a person be returned. If it is something that can be identified by a mark, such as an engraved name or a wallet with documents, it should be announced in synagogues and public places that an item was found, without giving any distinguishing details, so that it can be ensured that it is being returned to the rightful owner.
While the object is in the possession of the finder, it cannot be used and must be stored appropriately. It can be used if necessary for maintenance, such as occasionally starting an engine to prevent it from seizing up.
Only objects that cannot be identified, such as a banknote or a pencil, can be retained, provided we can assume that the owner has given up on finding them again.
One cannot perform one mitzvah by transgressing another; therefore, one should not hold up a wallet on Shabbat in the street.