Australian Open champion Jannik Sinner made light work of Christopher Eubanks to get his French Open campaign off to a bright start.

Italy's Sinner struggled with a hip injury in the build-up to Roland Garros but he moved well in a routine 6-3 6-3 6-4 win.

Sinner only looked troubled when serving out the match, handing his American opponent two break points with a double fault before recovering to seal victory.

"The hip is good, I am very happy," the 22-year-old said.

"The general shape is not at 100% yet so we try to build every day."

Greek ninth seed Stefanos Tsitsipas also won on Monday, beating Marton Fucsovics 7-6 (9-7) 6-4 6-1, despite much of the day's play being held up by rain.

Sinner will become world number one in Paris should defending champion Novak Djokovic fail to reach the semi-finals.

He put in a strong showing against Eubanks, hitting 33 winners and saving nine of the 10 break points he faced.

He will face home favourite Richard Gasquet next.