Actually it's a story of a writer(Ewan McGregor) and a courtisan(Nicole Kidman) who fall in love while they're preparing a play at the Moulin Rouge. They have to hide they're feelings from the play's investor, The Duke. It's not at all historically accurate. It's very artsy and the music is all redos from the 80's.
On a side note..Toulouse Latrec didn't have his legs amputated. He broke them when he fell off a horse when he was a teenager and they were stunted. Just so you know Hehehhe 😄 (Sorry, I just know a bit about Toulouse Latrec)