"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.

The inquiry, which is investigating claims of child abuse in Jersey's care system back to 1945, has heard evidence from 203 witnesses.
The next phase, in May, will hear from those who worked in children's services and those accused of abuse.
Chairman Frances Oldham thanked all those who had come forward and contributed to the work of the inquiry which started in 2014.
The now closed Haut de la Garenne children's home is among the island institutions at which accounts of abuse have been heard by the Independent Jersey Care Inquiry.
Ms Oldham said: "Whilst there have been some positive accounts, most of what we have heard has related to painful and damaging experiences.
"The first phase of the inquiry has been slow and painstaking, not least because of the difficulty many of the victims have had to wrestle with emotionally in terms of firstly giving a statement and then deciding whether to give evidence in public.
"We must establish the truth about how mistreatment of children remained hidden for so long and what was done when concerns were raised."
Chief Minister Ian Mr Gorst has set a deadline of December 2016 for the inquiry to conclude its investigations.

Cleveland Potash, which runs the site near Saltburn, said the development would secure the plant for 40 years.
Plans include extending the mine to the east and upgrading facilities to increase production capacity.
Some groups have raised concerns the development could have an intrusive effect on the local area.
The company hopes to extend its planning permission with the North York Moors National Park Authority to 2063.
Cleveland Potash's parent company Israel Chemicals Ltd (ICL) is set to invest Â£300m in the area over the next five years.
As well as funding the development of the Boulby site, the investment will go towards upgrading the company's Teesport operation near Middlesbrough, which exports potash mined at Boulby.
One of the first steps will be the Â£16m replacement of the tower at the top of the Boulby site's rock shaft, which lifts the mineral up from the mine.
The renewal will raise the amount of ore lifted to around 5.3 million tonnes a year, a one million tonne increase on the current maximum.
The mine's underground equipment, which Cleveland Potash general manager Phil Baines described as "aged", will also be modernised.
Mr Baines said: "Our present combination of potash resources and reserves totals around 70 million to 80 million tonnes, but following a major exploration programme we expect this figure will increase significantly over the new few years.
"Our plan is to extend operations out to the east in parallel to the area worked over the past 40 years, effectively providing a new mine for the next 40 years."
Acting heavyweight Alan Rickman is to attend the Glasgow Film Festival in support of his latest work.
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Jersey's child care inquiry has completed the first phase of evidence.
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Plans to extend a potash mine at Boulby in East Cleveland are expected to create more than 270 jobs by the end of 2015, the owners said.