"A Little Chaos" follows Kate Winslet's character Sabine, who is chosen to build one of the main gardens at King Louis XIV's new palace at Versailles.
Rickman plays King Louis in the film, which is his second outing as director.
The 11th Glasgow Film Festival will consist of 174 events, including 11 world premieres, and is set to run from 18 February to 1 March.
It will kick off with US writer and director Noah Baumbach's latest film, "While We're Young", starring Ben Stiller and Naomi Watts.
Force Majeure, which won the jury prize at Cannes, will be the closing gala.
Acting heavyweight Alan Rickman is to attend the Glasgow Film Festival in support of his latest work.