Eulalie

If you can count "un, deux, trois" in French, the "eu" sound in "deux" is what begins the name. My great-grandmother (b. Quebec, 1879) was named Eulalie. On her daughter's marriage license (Nashua, N.H., 1921), she was identified as "Leli." Nicknames common in the U.S. include "Eula," "Lily," "Lollie," and "Lee."

English Pronunciations: yoo-LAY-lee, yoo-LAYL-ee.

I've seen it with the pronunciation You-lily.

Here is an audio link to the proper French pronunciation to clear up any confusion about the yoo VS uu debate http://www.forvo.com/word/Eulalie/#fr

As far as I can tell, the British English pronunciation is YOO-lə-lee, and the American/Canadian English pronunciation is yoo-LAY-lee.

The pronunciation is uu-la-LI (see the key). The French "eu" hasn't an equivalent in English, but it's a bit like the "u" in "jump", for example. The name is very rare in France, and seems old-fashioned. [noted -ed]

Marie-Amelie's comment is right.
The French eu is pronounced UU according to the key, not YOO. It's kind of an 'err' sound. So, in French, it would be pronounced err-la-LEE. [noted -ed]

Actually, I believe the French EU is pronounced much like YOO, just like we normally pronounce it. If it was Ulalie, then you'd be somewhat correct but in French I believe it's pronounced yoo-lah-LEE. I take French in school. In English I would pronounce it YOO-la-LEE. Never yoo-LAY-lee. That reminds me of ukulele.

Pronounced eu-la-LEE.

It's pronounced yoo-LAY-lee.

...if it's French, though, the pronunciation is probably more like yoo-lay-LEE.