James was already making headlines for his freakish speech, which began with the actor denying Tommy Wiseau - the man he portrays in The Disaster Artist - a chance to speak after inviting him up on stage. "I don't wait for Hollywood, I make my own movie!"
The tweets have apparently since been deleted from Sheedy's account.
Franco, 39, who wore a Time's Up pin on his dinner suit, won an award on the night for Best Actor in a comedy or musical.
However, Wiseau's best friend, creative partner and author of the original Disaster Artist memoir has a slightly different narrative of the moment: Wiseau never wanted or expected to go on stage in the first place.
With The Disaster Artist, James Franco transforms the tragicomic true-story of aspiring filmmaker and infamous Hollywood outsider Tommy Wiseau-an artist whose passion was as honest as his methods were questionable-into a celebration of friendship, artistic expression, and dreams pursued against insurmountable odds.
Representatives for Franco and Sheedy did not immediately respond to TheWrap's request for comment.
"'Golden Globes, so what?" Actress Violet Paley claimed that Franco has once sexually assaulted her and even tried to entice her 17-year-old friend to his hotel room. Another actress, Sarah Tither-Kaplan, accused Franco of exploiting her in a film. At the time, Franco called it "bad judgment". But her timing couldn't have been more relevant, because the accusations are made against a man who is being celebrated and apparently supports the movement against sexual misconduct.
"I want to know what Tommy was going to say!"