This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
The people of Elfland know.
Travel back to Elfland and talk to all of them again. They'll tell you
what to do with the Floater.
4.2.9 -Final Fantasy I: I defeated Kraken, now what?
See 4.2.3. You now need to deal with the Lefeinish in order to get into
the Sky Castle to defeat Tiamat.