Give a “Les Miz” chick an award and she’s thinks she’s Marie Antoinette as ANNE guillotines rivals Katie Holmes and Claire Danes!

During hilarious skits on SNL, “Les Miserables” star Anne skewered both Katie AND “Homeland” actress Claire Danes. And although she’s of­fered a mea culpa to Claire – along with a bouquet of flowers – she’s conspicuously neglected to apologize to Tom Cruise’s ex-wife Katie.

“Anne and Katie are longtime rivals,” disclosed an insider. “Anne puts forth a very genial, friendly image, but she has a wick­ed competitive streak. She doesn’t like Katie because they used to go up for similar roles. Anne always felt like Katie used her Hollywood connections through Tom to advance her career. And she constantly makes fun of Katie behind her back, mocking her former marriage and even her appearance.”

Anne also believes she outclassed Katie in their “Batman” movies. While she was lauded for her performance as Catwoman in “The Dark Knight,” critics panned Katie, 34, for her role as the Caped Crusader’s love inter­est in “Batman Begins.”

“Simply put,” said the insider, “there is no love lost between Anne and Katie.”

Anne, 30, hosted “SNL” for the third time on Nov. 10, and while she also spoofed Claire’s erratic character on the Showtime series “Homeland,” her mean-spirited mockery of Ka­tie’s smile and manner­isms both infuriated and humiliated the actress.

And that wasn’t even Anne’s first roast of Ka­tie – she also mimicked her during a 2010 “SNL” appearance! While Katie – who, as The ENQUIRER recently reported, may be giving up acting for law school – was good-natured the first time around, she’s apparently not laughing anymore.

“It all comes down to the fact that Anne doesn’t take Katie seriously as an actress,” noted the insider. “And Katie’s gotten Anne’s message loud and clear.”