Nowadays it's mostly only the case on the letter <e>, where it indicates a pronunciation of /ɛ/.

In the past, when put on a <a> it changed it from /a/ to /ɑ/, however that mostly fell in disuse in most French French dialects and I can only hear the distinction consistently in Canadian French dialects.

Once upon a time, it did and in some varieties still does: its origin was in a lost /s/ (later other deleted consonants too, IIRC), which lead to compensatory lengthening of the preceding vowel. You can still see this in some varieties of French, such as Belgian and Swiss French, which preserve the old long vowels somewhat better than metropolitan French.

That's the thing, this specific reform only removes the accent when it doesn't have any impact. It's really about cleaning up inconstencies and weird edge cases.