Je m’en fiche éperdument!
zhmah fee shay-pair-dew-MAH! Click below to hear this.*
I couldn’t care less!
The French word éperdu has many related meanings, all of them stemming from a 16th-century word meaning to lose completely. It can translate as distraught, overcome, wild, frantic, passionate, and more.
As for Je m’en fiche, it’s one of several ways to say I don’t care. In order of forceful language from least to most, you can say Je m’en moque, Je m’en fiche, Je m’en fous. They are the equivalent of I don’t give a rip/a rap/a fig, I don’t give a darn, and I don’t give a damn. None is actually considered vulgar, and the first two can be said in the politest company (though perhaps you should abstain from arguing in such company).
Adding éperdument simply reinforces your feelings, rather like saying I am wildly indifferent. It’s about the equivalent of I couldn’t care less.
And by the way, a word of caution about that English: saying I could care less, as so many people do, states the opposite of what you mean: I don’t care much, but if I work on it, I could manage to care even less. I couldn’t care less means I already don’t care at all, so it’s not possible to care less than I do now. If only for the sake of my sanity, please try to care about that, at least.
*Some mobile phones, such as Blackberries, won’t display the audio player. If no player appears, here’s an alternative link to the audio file: