Britney Spears has a fan in Sofia Coppola ... she recalled the pop superstar's infamous umbrella incident back in the early aughts as a "punk moment," and a symbol of women's rights.

The renowned director applauded Brit during a new chat with Elle, fondly recalling the moment a bald Britney attacked a paparazzo's car with an umbrella in 2007. She raved ... "She’s become this symbol of women’s rights. That would never happen to a man."

Sofia did not specify what "that" means, but we all know the Princess of Pop went through it in 2007 ... with a series of public outbursts leading up to her former husband, Kevin Federline, winning custody of their two sons. And she was notoriously placed under a court-ordered conservatorship in February 2008, which lasted for 13 years. As for Britney now ...

And as you know, Britney was back in the headlines -- not for her signature dancing videos she posted on Instagram -- but for being arrested for a DUI earlier this month. She's been hanging low since ... but we were told at the time that those around her want a mental health and detox treatment plan.

Brit's court hearing for her arrest is May 4.

Sofia also said she would be interested in working on a project about Britney's life ... though Jon M. Chu was slated to do so in 2025. No major developments have been announced, so perhaps she'll be "Lucky" enough to get her hands on it!