The action on Court Simonne Mathieu and the other outside courts had been interrupted for five hours since just before midday local time before the decision came to call off the matches.
"Due to the poor weather conditions, all remaining matches scheduled to take place today on Simonne-Mathieu Court and the outside courts have been cancelled," the French tennis federation said in a statement.
It added that ticket holders for the courts affected would be entitled to a full refund given there had been less than two hours of play.
Only matches on the Philippe Chatrier and Suzanne Lenglen courts, which both have a retractable roof, were able to go ahead as scheduled.