The Louisiana Purchase was the latter, a treaty. The Constitution specifically grants the president the power to negotiate treaties which is just what Jefferson did. It is true that the Constitution does not specifically authorize Congress, let alone the executive branch, to purchase land from other nations.
Having failed to end with Haitian Revolution and the possibility of more war between France and England, made Bonaparte decide to sell Louisiana to the United States, in order to finance his military operations. Jefferson saw the purchase as the possibility of a very important acquisition of land for the United States.
