Italian cinema great Marco Bellochio, 76, saw his latest film "Fai Bei Sogni" (Sweet Dreams) chosen to open the increasingly prized sidebar competition, after being snubbed in the Palme d'Or selection.
The film about a boy coping with the death of his mother is his first to be shown at Cannes since "Vincere" (To Win) was shown in the main competition in 2009.
The other two Italian films are "Fiore" by Claudio Giovannesi, set in a juvenile detention centre, and "La Pazza Gioia" (Like Crazy) - about two patients who escape a mental institution.
They are among 18 feature films chosen for the Director's Fortnight, which often offers up some of the most raved about films during Cannes.
"This year there is a mixture of the veterans, Jodorowsky, Bellochio, and the youth," said Director's Fortnight artistic director Edouard Waintrop.
Chilean director Alejandro Jodorowsky, 87, will present his autobiographical feature "Poesia sin Fin" (Endless Poetry).
Another film initially slated to be included in the main competition that ended up in the Director's Fortnight is "L'Economie du Couple", a tale of a divorced couple who continue to live under the same roof for economic reasons, by Belgian director Joachim Lafosse.
Chilean director Pablo Larrain's "Neruda", starring Gael Garcia Bernal as an inspector hunting for poet Pablo Neruda, who became a wanted man in Chile in the late '40s for his communist sympathies, also got the nod.
Indian director Anurag Kashyap - who directed the acclaimed psychological thriller "Ugly", shown at Cannes in 2013 - returns to the genre with "Psycho Raman" about a serial killer terrorising Mumbai in the '60s.
American director Laura Poitras, who won an Oscar for "Citizenfour" about fugitive US intelligence whistleblower Edward Snowden, will be showing her latest documentary "Risk" focusing on Wikileaks founder Julian Assange.
The independent competition will end with "Dog Eat Dog" by Paul Schrader, director of the 1980 crime drama American Gigolo and author of numerous screenplays for Martin Scorsese films, including "Taxi Driver".
Starring Nicolas Cage and Willem Dafoe, "Dog Eat Dog" follows three ex-cons trying to adapt to life outside bars.
The traditional animated film entry will this year be Claude Barras' debut "Ma Vie de Courgette" (My Life as a Courgette) about a nine-year-old boy making it in a foster home after his mother's sudden death.