It was a few years before I encountered serré(e) and serrer.
Serrer has a number of meanings related to tightening, (en)closing, or being close to something. It took me a while to get that, though, because I first encountered this word in the phrase serrer la main de quelqu’un — to shake someone’s hand. However, serrer gets this meaning because in order to shake someone’s hand, you first have to clasp it.
Serré(e) is the past participle of serrer and an adjective that means tight, close, or crowded. It also can be used to describe very strong coffee, as seen at the end of this bande desinée.
Finally, I thought I’d mention une serre, which is a greenhouse. I’m not sure if the words are related, but my mnemonic for remembering these words is that a greenhouse is an enclosed, protected structure for growing plants.
Hibiscus growing in a greenhouse (une serre) at Longwood Gardens