Literally means someone who wields a fag. As a musketeer holds a gun, a fagoteer has a fag or cigarette. Translated into modern terms: a smoker; someone who smokes.
Not to be mistaken by fag or faggot. This word has nothing to do with sexual preference at all.
John: Dude, I can't breathe in yo momma's house, she's more a fagoteer than I thought!