Venus and Harrison broke early in the second set and gradually got on top of the duo who had both played five set singles matches the previous day.
"It was just execution, we were giving too many free points away but I have to give credit to them, they also played some great shots. We changed some of our tactics and it worked well in the end so I am really excited."
Venus and Harrison could potentially face the fourth seeds Lukas Kubot and Marcelo Melo in the second round. They play their first round match tomorrow.
"The last three years I have been looking at flights about this time to get out of here, so it is nice to be here a bit longer, but plenty of work to do so I need to get out onto the practice court and fix some things."
Marcus Daniell and Artem Sitak open their campaigns overnight.
Daniell and Brazilian partner Marcelo Demoliner have been pitted against the 7th seeds, Croatian Ivan Dodig and Spaniard Marcel Granollers.
Sitak and his American partner Nicholas Monroe open against the 12th seeds, Poland's Marcin Matkowski and Frenchman Eduard Roger Vasselin.
Matt Brown is in Paris thanks to Emirates Airline