d'Arrast was born a British subject, in Dublin, Ireland, from a partially Basque noble family of the French province of Soule. His father, Michel Abbadie, was born in Arrast-Larrebieu and his mother was Irish. His grandfather Jean-Pierre was a lay abbot and a notary in Soule. The family moved to France in 1818 where the brothers received a careful scientific education. In 1827, Antoine received a bachelor's degree in Toulouse. Starting in 1829, he began his education in Paris, where he studied law.