On "Gilmore Girls," Michel Gerard is fearful of swans because a flock attacked him when he was a child. The story is one of Michel’s amusingly specific personal fears, fitting his dramatic, easily irritated personality.
Michel, played by Yanic Truesdale, is the French-born concierge and manager associated with the Independence Inn and later the Dragonfly Inn. His polished manners and sophisticated tastes contrast with his frequent complaints, sharp sarcasm, and dislike of many ordinary situations. The swan incident is mentioned as part of the character’s backstory rather than as a major plot event.
A common mix-up comes from another television character: Jess Mariano is also famously attacked by a swan in the series. That parallel helps make the answer memorable, but Michel’s fear is specifically tied to being attacked by swans as a boy. The show does not mean geese or ducks; swans are the canonical answer.