We finally have, via Variety, the first look of the film directed by Todd Haynes, which will have its Premiere in the official section of the Cannes festival:

The Variety article also provides us with a first official synopsis of the film:

Moore and Melton star as married couple whose 20-year relationship inspired a national tabloid obsession at its offset. Now preparing to send their grown children off to college – as Melton reconciles with empty nest syndrome in his mid-30s – an actress (Portman) embeds with the family to study them for an upcoming film where she’ll play Moore. The couple buckles under the pressure as Portman probes as deeply as she can for an honest performance.

The film can be seen in just three weeks in Cannes…