A patrol of two officers asked three women who were bathing topless on the beach of Sainte-Marie-la-Mer on August 20 to cover up with their swimsuits.
Police said the request followed a complaint from a nearby family who were embarrassed by the situation due to the presence of their children.
Interior minister Gérald Darmanin spoke out in support of the women on Twitter saying: "Freedom is a precious commodity".
He added that it was normal for the administration to recognise its mistakes.
The Pyrenees-Orientales police said in a statement shared on Facebook that no "municipal order forbids this practice in Sainte-Marie-la-Mer".
"Guided by a desire for appeasement, the police asked the people concerned if they would agree to cover their chest after they explained the reason for their approach," it said.
Police spokeswoman Maddy Scheurer blamed the "clumsiness" of the two officers for the incident on Twitter.
She said: "You will always see me in uniform, but the practice of topless tanning is allowed at the beach of Sainte-Marie-la-Mer."
One social media user disagreed and said the incident shouldn't be blamed on the "clumsiness" of the officers but on "incompetence".
Others questioned how the patrolling officers were not aware of the law which does not forbid the practice of topless bathing at the beach.
"I dare to hope that this poor woman received a formal apology," said one Twitter user.
It is not illegal to sunbathe topless in France, but local authorities can ban the practice with guidance about clothing.
