Of course when I said "wrong," I meant "in a way that doesn't really work for you." You can pronounce it any way you want, and even with my Classical education, I don't pronounce every name in the books "accurately" (too much work). But, even though I like the name Irene in all its different forms, I too felt that I couldn't pronounce it as if singing "Goodnight Irene," so I played around with it in my mind's ear and went more Greek with it, and after that it seemed perfect.
Sure, eye-ren-ay could work, or ee-ray-nay (closer to the Greek), or even the more British eye-ree-nee.
The French would be more like ee-REHN. Only Frenchier.
Just find one that reads more naturally for you. Enjoy.
-Philia