After two fiercely-contested opening sets between the two unseeded pairs, Harrison and Venus broke decisively for 5-3 and held serve to prevail on Court Philippe Chatrier.
It was the pair's first major final, Harrison having never reached the last four in a grand slam while his partner had never even been in a quarter-final.
“Ryan, thanks for playing. I am not very good at this," said the 29-year-old Venus, who became New Zealand's first male grand slam winner since Onny Parun teamed up with Australia's Dick Crealy to win the 1974 French Open.
"To all the people back home, I got lots of messages and support. To all my family watching, my mom is here watching, I wouldn’t be here without you."
Venus and Harrison teamed up ahead of the clay-court season earlier this year and won their first ATP tournament in Estoril last month.
(Reporting by Julien Pretot and Hardik Vyas in Bengaluru; Editing by Clare Fallon)
