Another issue with Briar, is that it means "thorny patch" this isn't the most promising meaning for a child. When used with Rose (Briar Rose, as in Sleeping Beauty), it gives the sense of beauty in the midst of struggles, but by itself...
Here are some other ideas:
Capucine -French for nasturtium, used as a name in Europe (at least, I once met a woman from Belgium with this name)
Jonquil -French for daffodil
Phoebe -cute little bird http://en.wikipedia.org/wiki/Eastern_Phoebe
Slate -although, this sounds a bit too masculine for me
Names that have nature meanings:
Petra -rock, stone