Holy crap I've never gotten one of these before. Alright lemme try my hand at the explanation.
Telon
You’re a help in a pinch, rest azured
The Blue Narciss is used by the party to escape the attack on Alexandria. Azure is a play on words in reference to the color of the wings and the name of "Blue" Narciss.
Telon
And you’re driven by not a word
This is another play on words. The ship is piloted by Blank, whose name is, by definition, not a word, as 'blank' is often substituted for a missing word. I.e. fill in the blanks.
Telon
Though vain you must be
With us not with thee
I'm not totally sure on this one, but I think it's another play on words. Vain is another word for Narcissistic, the root word for the name 'Narciss' in Blue Narciss. The clue states the Narciss must be with us (the party) instead of by itself in order for them to escape the attack.
Telon
Shall I see you again on the third?
Regent Cid is so impressed by the boat's power, he uses parts from the ship in the third model I his airship, Hilda Garde III.
Oh, and the hints refer to one game (IX), a non-living object (a boat), and the last clue is lyrics to the song "I'm on a boat". Never would have gotten this if not for that last one. Almost guessed the White SeeD ship actually. Glad I changed my answer.