Preliminary charges have been filed against the parent company and its chief in France following a criminal probe that was opened last year, court sources and people familiar with the case told AFP on Wednesday.
Equivalenza was not immediately available for comment.
The company's website says it opened in 2011 with the aim of providing consumers with a range of high quality fragrances at affordable prices. It produces perfumes itself and sells them in unlabelled bottles that clients can have refilled.
The probe focused on charts the company produced to help its sales staff advise customers when asked for a fragrance similar to a leading brand, one of the sources said.
The company, which is present in some two dozen countries, has vigorously denied counterfeiting allegations, the source added.
The filing of preliminary charges in France does not mean that a case will necessarily go to court. France, a leader in the luxury industry, aggressively combats counterfeiting.
The nation's federation of beauty companies, Febea, recently estimated that around 10 percent of total counterfeits are cosmetics, a sector which generated €10.9 billion ($12.2 billion) in sales in 2013 and was among France's top net exporters.