The main reason you can’t sing the blues in French? The language won’t let you.
“Je reveillais ce matin” is French for “Woke up this morning”. The accent falls on the wrong syllable. None of the vowels sound right. You have to hold your lips just so.
Instead of the Blues the French have L’Existentialism, which was invented by intellectuals.
Instead of the Blues, the French have joie de vivre, which isn’t as sappy as it sounds in literal translation. No one expects the French to smile if they are not amused.