The retailer advertised reductions on products on which the final sale price was "substantially the same" as the pre-discount price and blocked orders from customers who had previously returned more than a certain amount of purchases, the regulator said in a statement.
YNAP did not immediately respond to an emailed request for comment.
The regulator said the violations took place between 2019-2022.
The business was controlled by Swiss luxury group Richemont until last year, when it sold a majority stake to luxury e-commerce specialist Farfetch and Dubai Mall developer Mohamed Alabbar.
($1 = 0.9229 euros)
(Reporting by Alvise Armellini; Editing by David Goodman)