Trompe l'oeil.

It's a bit similar to the "loy" in the word loyal, if you're speaking English. In French it sounds like this: http://www.howjsay.com/index.php?word=trompe-l%27oeil&submit=Submit

Thank you Diana. The French pronounciation sounds like tromp-play, so that is how I shall say it.

tromp-ploy would be much better.

How to say it might depend on the audience. Pronouncing it as in French might be less understandable to an English-spekaing audience, or might even get you some snob or stickler who sneeringly corrects your pronunciation. (There are always someone who will insist on a French pronunciation of a term that is still spelled as in the original French.)

Oxford give BrE and AmE pronunciations

Well, I'm British and I've always said it the French way. I always assumed people that said Tromp-loy were in error. Might be because I first came across the phrase in English when I was already studying French at school.

If you change the "aw" sound in the middle of loy to a (non-rhotic) "er" sound, that would be a movement in the right direction.

It is also a bit similar to the sound written äu in German, if you know about that.

It is probably unhelpful to point out it is also similar to the au sound in Icelandic. Indeed exceptionally unhelpful in the sense that many "how to pronounce Icelandic" lists explain au as being "rather like oeil in French"...

Thanks all. Now I am thoroughly confused!!

The point is that if you pronounce L'oeil as loy, your French would sound about as convincing as Inspector Clouseau's pronunciation of English (as played by Peter Sellers in the Pink Panther films): it would probably be understood, but it would be heard has as having an English accent of almost comic extremity.

If you are very familiar with the Pink Panther films, you might recall how Inspector Clouseau pronounced the word "bomb", as it was a point that was particularly hammed up as he had to repeat it a few times until he was understood. The sound that Clouseau was using there is very close to the vowel sound you want at the start of oeil. If you take taht sound instead of the first vowel sound in loy, you'll be much closer to correct French.

It's the first time I've been accused of sounding like Clouseau!

To be fair, I did say that it was a bit similar to "loy" and didn't say "it is exactly the same thing." I thought that advanced topics of exact pronunciation might not be useful to someone who is just beginning to say the word.

We have no indication that the OP plans on saying this in a French conversation---it sounds to me like she's trying to use it in English--and a French sample was provided in case she is actually going to be speaking French. How much French you use in your English is a personal decision, but not all people like to switch into fluent French for a two-word phrase, especially if the person they're talking to doesn't speak French.

I don't know how differently you personally pronounce äu from the sound in "loy[al]" but even if you do find a minute difference in there, I can't imagine that's useful to the OP without a lot more explanation. The wiki page for German IPA uses the English word "boy" as the approximation of äu.