The definition of méchant is "mean", as in "mean-spirited", but how did it get this meaning? A quick search of its etymology shows that it probably derives from the Old French verb cheoir, which means to "fall out" or "become detached". I can see how mean-spiritedness is a kind of falling out... but is that the connection which led méchant to acquire its meaning?
The prefix "mé-" means "in a bad, negative way" (ex: médire, mécontent, méconnaissable). So mé+chéant would mean "who falls in a bad way", that leans a bit towards the current meaning. Look also at the French article of wiktionary.