We still read Montaigne so many years after his death in September of 1592. Why shouldn't we still read this biography, from 1962, from Montaigne's devoted translator and biographer, Donald Frame? His scholarly work demonstrates his knowledge, his understanding and his appreciation of Montaigne's work.
While convinced that you need not go any further than Donald Frame, we will advice the potential reader that your devotion to the book might wax and wane. Devotion to the life of a philosopher from the 16th century might be more than most can muster.
This is not an easy introduction to Montaigne, so it is not recommended for those who are unfamiliar with the man or his work. Frame is an eminent Montaigne scholar, so he integrates very well and very often excerpts from Montaigne's writings into his life story.