Generally speaking, movies that play at the Cannes Film Festival in May don’t win Oscars. It’s a long year and it isn’t easy for a film to use the hype from Cannes to keep it going to have an impact much later in the year. A movie has to be really special to to get the attention of Oscar voters. 
The films in the last 10 years that have received a Best Picture Oscar nomination are:

No Country for Old Men – 2007
The Artist – 2011
The Tree of Life – 2011
Midnight in Paris – 2011
Amour – 2012
Nebraska – 2013
Mad Max: Fury Road – 2015

The Artist went on to win Best Picture. It was much easier for these films to get in when they allowed 10 Best Picture nominees. Tree of Life was booed at Cannes, but being underestimated can make an Oscar film. 

Often when a film does well at Cannes, it doesn’t finish out the year with a Best Picture nomination. It can help to spring up acting and writing contenders. Like Cate Blanchett and Rooney Mara in Carol or Steve Carell in Foxcatcher. Last year at this time we were convinced that Ruth Negga and Loving were shoo-ins for a Best Actress and Best Picture win. 

A few films that played at Cannes this year have some buzz. Todd Hayne’s Wonderstruck, probably being the most talked about. Other possibilities include, The Killing of a Sacred Deer, Good Time, You Were Never Really Here, The Meyerowitz Stories and The Square. A Smaller film like The Florida Project, is prime for a Spirit Award nomination. A few foreign language films could break through like, Loveless, Jupiter’s Moon, White God and Happy End. 

It’s all worth paying attention to, but certainly don’t draw any conclusions this early in the year. The real test comes in the Fall with Toronto, Telluride and Venice.