Burel, ranked 45th in the world, was defeated 7-6 (7-2) 6-1 by former world number one Osaka.
Since defeating Victoria Azarenka at the 2019 French Open, Osaka has not triumphed on clay against a player ranked in the top 50.
In the second round on Thursday, the 26-year-old, who gave birth to her first daughter a year ago, will take on Marta Kostyuk of Ukraine, the 19th seed.
Dan Evans of Britain will have to wait to play Italy’s Fabio Fognini in the men’s division as his first-round match was postponed on Wednesday due to bad weather in Rome.
