Well, it did back in the 18th century when the left/right split was first named and well into the 19th - it represented the split between monarchists and opponents in the French assembly after the revolution, and so the liberals made up most of the original left.
You see the after-effects in e.g. Norway, where the liberal party is literally named "Venstre" ("Left")
It's just that most places the liberals have been firmly out-flanked on the left since.
