Port-au-Prince was built in 1749 and , in 1770 , it replaced Cap-Fran Ã ais ( the modern Cap-Ha Ã tien ) as capital of the French colony of Saint-Domingue . In 1804 , it became the capital of new independent country Haiti . In 1770 , Port-au-Prince replaced Cap-Fran Ã ais ( the modern Cap-Ha Ã tien ) as capital of the colony of Saint-Domingue , and in 1804 , it became the capital of newly independent HaÃ ti .