The French shoe company filed the lawsuit in U.S. District Court in Manhattan in April against Yves Saint Laurent S.A.S., another French company based in Paris.
A federal judge denied Louboutin's request for a preliminary injunction. The parties have been ordered back to court next week.
The lawsuit states designer Christian Louboutin originated the concept of red soles in its shoes as a trademark nearly 20 years ago. It says he created the idea when he painted red nail polish on the black soles of a pair of women's shoes.
YSL did not comment on the suit.
The Associated Press contributed to this report.