The pair are among 18 film-makers vying for the prestigious Palme d'Or at the annual film industry get-together.
Loach's Jimmy's Hall is based on the true story of an Irish communist who ran a dance hall, while Leigh's Mr Turner is a biopic of painter JMW Turner with his regular collaborator Timothy Spall in the title role.
Both Loach and Leigh are regulars at the festival and previous winners of the Palme d'Or.
Leigh won it in 1996 for Secrets and Lies, while another of Loach's films set in Ireland - The Wind That Shakes the Barley - won a decade later.
Jimmy's Hall will be Loach's 18th film to be shown at Cannes since he made his first appearance there in 1970 with Kes. He has also directed films such as Sweet Sixteen and My Name is Joe.
The festival opens with a Grace Kelly biopic called Grace of Monaco starring Nicole Kidman as the princess and Tim Roth as her husband, Prince Rainier.
Director Jane Campion, the only woman to have won the Palme d'Or, is leading the festival's jury this year for the competition on the Riviera resort.