The Washington Post runs an article with the title "Why Foreign Troops Can't Fight Our Fights." As it notes, foreign troops are often proposed as a solution but seldom actually work well in practice.
As COTTonLINE has repeatedly written (search if interested), the U.S. is often involved in places where a foreign legion would be useful. With American officers, third world enlisteds and NCOs, it wouldn't be prone to weapon turnover and side-changing as local forces often are.
Like the French version, these would be U.S. troops, earning citizenship upon retirement if they chose it. The acculturation aspects of a U.S. foreign legion would be considerable.
It might also be wise to adopt certain aspects of the British experience with third world colonial troops. That is, recruit a regiment (or larger unit) from each region, where a unit's troopers would share language, ethnicity, perhaps religion, and food taboos. This worked for the Brits in Asia and Africa.
