Szeps was born in Lausanne, Switzerland. Due to the German invasion of Poland, his parents fled to France. His father left the family to join the French Resistance, and his mother and three-year-old sister made their way to a refugee camp in Lausanne, where Henri was born. He spent a lot of time with foster families, and later at a French orphanage, before coming to Australia at the age of eight with his mother and sister.