The expression prendre la mouche literally translates into 'taking the fly', as in the annoying insect that buzzes around your house in our typical North Carolinian summer.
If someone says tu prends la mouche, they are however not asking you to grab a fly, but rather accusing you of getting angry with no good reason. Someone who prends la mouche is someone who gets ticked off easily. The reason behind their vexation is stupid, trivial or close to non existant, and seems to come out of nowhere. If you remember the last time a fly landed in your ear, you'll picture the sudden reaction of irritation you got, while people around you might have wondered what was wrong with you. That's the idea.
Prendre mouskes is an old expression dating all the way back to the 14th century when mouske was a generic term for any annoying flying insect, such as mosquitoes, wasps, flies and gnats, to name just a few. Mouske became mouche in the 15th century, and still described all kinds of buzzing bugs. It also took the metaphoric meaning of “a burden, a negative thought that appears suddenly out of nowhere."
At the time, the verb prendre could mean to feel the effect of, as in other expressions dating back to the Middle Ages, such as mal/bien prendre quelque chose - to take something the wrong/right way, or prendre ombrage - to take umbrage.
Il prend souvent la mouche pour rien.
He often gets angry for nothing.
Mon mari prend toujours la mouche quand il rate les sorties sur l’autoroute.
My husband always flies off the handle when he misses exits on the highway.