What is the prescribed legal retribution for someone who attempted to commit adultery with a neighbor's daughter in a country that does not apply Sharia law?

If the act was merely an attempt at fornication without penetration, it is a sin that warrants ta'zeer (discretionary punishment) not hadd (prescribed punishment). The perpetrator is only subject to hadd if penetration occurred and this is proven by sharia-compliant evidence. In all cases, hudud and ta'zeerat are solely within the authority of the Imam or his deputy.