Listening to Edith Piaf, it struck me for the first time that it doesn't make sense to parse "Je me fous du passé" as something about madness. The literal meaning has to be something surprisingly vulgar, at least to English sensibilities.
I put the phrase into Google Translate and it came up with "I care about the past". That doesn't make sense either. So I put a line break in after "fous", and it changed to "I do not care"/"the past".
I deduce that "I don't care about the past" is an acceptable translation, and that Google Translate est fou et foutu. But in a good way.