For what it's worth I'd go with "john vee ev", as I've seen Genevieve spelt with a grave accent (sloping this way \ ) as it *is* French in origin. I also remember reading an article about Alison Moyet years ago in which she said that she used her middle name as she was sick of people mispronouncing her first name which is actually... oh well, you know the rest,
That said, the more commonly heard version as far as the UK's concerned is "jen a veev" which is most likely related to the 1953 film of the same name which probably brought on all the confusion in the first place!