You can only pick up the driftwood if: Nancy commented about CouCou's perch.
Then you talk to CouCou about her perch. After giving her a guava, she says she wants a driftwood perch.
After the bird asks for a perch, then you can pick up driftwood.
There are several at 3 beaches.
You get one, show it to the bird until she approves what you bring. This is a random puzzle.