Henri is a boy's name, and I can't get Eddie to work for even a spunky girl. But Edie packs a nice punch, I think. Among your choices, I love Tess and Clio and Pip or Piper. Pip could short for either Philippa or Penelope. Liza, Lola, and Live are great. I second Goldie too.
How about Dana, Coco, Nina, or Rita? (Coco could be short for lots of names if you prefer it as a nickname instead.)