Is it permissible, in Islamic law, to take a 10% share of money found and handed over to the police, and is this percentage legally sanctioned, and does the one who takes it incur sin?

If the owner of the money pays a percentage to the finder willingly, there is no impediment for the finder to take it, because the owner has the right to dispose of his property. However, if the owner pays it unwillingly, but because the law obliges him to do so, then that does not make it permissible to take people's money without their consent.