LORELAI: Michel, we’ve been over this, we all cover the phone, that includes you.
MICHEL: Don’t misunderstand. I want to answer it, I truly do, but today, today I am suffering from ennui.
Ennui is the French word for boredom and lethargy, with connotations of a melancholy world-weariness, and the jaded feeling of having life a little too easy. It has a particular resonance in twentieth century existentialist literature, such as by Kafka, Sartre, or Albert Camus, which often centres on a protagonist who drifts through life in the grip of ennui, angst, and alienation.
Lorelai has absolutely no patience with this, and diagnoses Michel as simply being tired, for which she prescribes (of course) massive amounts of coffee.