How do you pronounce une plume?

"ewn plewm"

The French "u" sound is the same as the French "i" sound (which sounds like "ee" as in "beep" but tighter) but with rounded lips, so that to us English speakers it sounds sort of like "oo" as in "loop". However, don't confuse "u" with "ou". Otherwise you might end up talking about your cul ("kew" - ass) when you mean your cou ("koo" - neck).