Being one who was blessed with a French name while living in the USA, I would like to add that the what is accepted as the proper pronunciation has a lot to do with where you're from or where you are at the time.
I say my name as my relatives in Montreal pronounce it, with the "ier" pronounced as "a". And my first name pronounced more like Michelle then the Anglo Michael (with the ch pronounced like a k) But many Fournier's (which is a much more common name then you would think) pronounce it like Four-ni-err it drives me nuts. A lot of people think I am being pretentious just because I use the French pronunciation of my name. I even grew up with teachers trying to correct me I would say my name as Michelle Fourn-a and they would say you mean Mi"K"ael Four-ni-err; after a while I just gave up. Also Pelletier is another French name that many here in the US do not pronounce correctly. But the same people will pronounce Mark Mesier's name just fine and they all pronounce "Cartier" correct as well. I always joke I guess you have to win a Stanley Cup or be a jeweler to get your name pronounced correctly.
Well at least when I visit relatives in Canada, I get to hear my name correctly. But since my family did not speak French at home (only my father is French) I never learned much beyond how to say my name, and the swears my father would mutter when he hit his thumb with a hammer or something. Also I always knew I was in trouble when I heard my dad yell my full name in French followed by a bunch more French I did not need to understand to know the meaning of.
If you are French the o sound at the end is just "o" (rather truncated sounding) not like "ooh" as some might say. It's not easy to really say French names correctly with a American English accent - you start to sound like you are imitating Peter Sellers as inspector Clouseau. (another name with that "eau" at the end.
