From childhood he accompanied his father on trips abroad, where he received education and studied several European languages. In 1722 he received the rank of the chamber junker and was appointed adviser to the embassy in The Hague. However, in May 1722 he was sent to the French court, where he acted together with his father, who accompanied him as a private person. Kurakins managed to achieve the assistance of France in maintaining peace with the Ottoman Empire during the Persian campaign. In 1724, Boris Ivanovich Kurakin was appointed Ambassador Extraordinary and Plenipotentiary to France, Alexander Borisovich Kurakin was appointed a representative at the French court with the award of the rank of chamberlain (May 15, 1724). Diplomats were given the task of obtaining consent for the marriage of Princess Elizabeth to King Louis. However, this project failed. He patronized Vasily Trediakovsky, who studied abroad, who dedicated to him his translation of the poem "Riding to the Island of Love". After the death of his father in 1727 he was appointed ambassador in Paris. Ernst Munnich in his "Notes" wrote: