In my experience, songs in English that are authentically "traditional" always have a regular rhyme scheme. Sometimes the rhymes are no longer exact because the pronunciation of some words has changed over the years. Also, traditional songs always have a simple, regular metrical structure. It is only in recent times (late 20th century, anyway) that singer-songwriters have taken to writing songs that resemble free verse.

Regular rhymes and regular rhythm make a song easier to memorize. And they provide a check on your memory. If what you "remember" has a faulty rhythm or rhyme, it's a clue that either the song is of recent origin, or your memory is faulty.