exotic you have just reminded me of another reason we didnt use it! we were going to use the english version but dp's aunt used to live in geneva and she insisted on pronouncing it the french way in a really twee voice with an annoying tone, when she did it dp and i just looked at each other and knew it would drive us insane forever more! so that and the fact that it is VERY likely to be shortened to jen/jenny is why we didnt use it.
we are very happy with our dd's name, but genevieve is a really lovely name, so its a shame that one annoying relative and the shortenings mean we wouldnt use it. but htat was something we thought about when naming ours, the shortened versions as they inevitably end up being used, particularly at school age and we wouldnt choose a name that we didnt like the shortened version of.
i do like ginny or vivi tho, but i still think it is more likely to end up us jen/jenny once they get older.
basically if you are happy with the shortenings then go for it, it is a lovley name :)