Do like most people these days: learn song lyrics! Songs are really poetry. Some have very deep meaning and good flow. Some will probably resonate with your own feelings.

Otherwise I have only bad recommendations in French, but I learned almost all of Cyrano de Bergerac's play and still remember maybe a third of it. In it, "La ballade du duel" flows very well and "la tirade des nez" is a classic that is a very good exercise.

I have no clue about English poetry. Despite having a decent written English level, I could never get into poetry in English. I think my pronunciation is not good enough and I have a hard time knowing how some more rare words, common in poetry, are actually pronounced. I would love to have the courage to get into Paradise Lost at one point.