From the "Etymological Dictionary of Biblical Hebrew"
The root of מלא is מ-ל-א = "fill to abundance",
The root of מלאך is ל-א-ך = "serve; work which completes goal".
There are many examples in Hebrew where the first letter is "mem" which is not part of the root: מקדש, מגדל, מחשב, מגהץ, etc.