I can't for the life of me figure out how to say pyöreä.
You mean you don't know how it sounds, or you can't produce that sound? Here's an example: https://forvo.com/search/py%C3%B6re%C3%A4/.
pyöreä has the IPA value of /ˈpyø̯re̞æ/. I like to break it down as sounding like “peu-rey–ah”, with the peu in French phonology.
You seem to have lost one syllable with your French lifehack ;-)