Here are some classics that I would recommend:

France
A bout de souffle (Breathless) - Jean-Luc Godard
The 400 Blows - Francois Truffaut
A Man and a Woman - Claude Lelouch

Italy
The Bicycle Thief - Vittorio De Sica
L'Avventura - Michelangelo Antonioni
La Dolce Vita - Federico Fellini
