Twenty-second Amendment to the United States Constitution
Some argue that the 22nd Amendment and 12th Amendment bar any two-term president from later serving as vice president as well as from succeeding to the presidency from any point in the presidential line of succession. Others contend that the original intent of the 12th Amendment concerns qualification for "service" (age, residence, and citizenship), while the 22nd Amendment, concerns qualifications for "election", and thus (strictly applying the text) a former two-term president is still eligible to "serve" as vice president (neither amendment restricts the number of times an individual can be elected to the vice presidency), and then succeed to the presidency to serve out the balance of the term (though prohibited from running for election to an additional term).
French nationality law
In 2001, as Bill Clinton finished his second term as President of the U.S. (the legal limit of terms under the U.S. Constitution), a theory was published by CNN that he could claim citizenship of France and run for leadership there. The open-letter by historian Patrick Weil held that a little known "law, passed in 1961 [article 21-19(5º)], enables people from former French territories to apply for immediate naturalisation, bypassing the normal five-year residency requirement for would-be French citizens." As Clinton was born in Arkansas which had been part of French Louisiana before it was sold to the US, it was held that he would qualify under this law. And as a naturalised French citizen, he could run in the French presidential election.