Pharr (Homeric Greek: a book for beginners, 4th ed.) has on pp. 10 and 281 a statement that μῆνις in Homer would have had an α in most dialects and says that it's cognate with maniac and maniacal. But looking at the English wiktionary etymologies it seems hard to tell what's going on. Is the relatedness of these words right, wrong, controversial, or unknown?
On a side note, it's interesting that at least according to some sources, "menace" also comes from a PIE root mon-, but there are two such roots, and it's a different one. It's cognate with "mountain."