French social networks exploded with anger after a young woman was reportedly beaten up by a gang of girls and young women for wearing a bikini in a park.

Authorities have not identified the attackers but most commentators have assumed that they were Muslims.

Protesters organised a demonstration in bikinis and other bathing costumes in the park where the attack occurred, in Reims in northern France. Although drizzle and cold winds meant only about a dozen people turned out, hundreds across France responded to a Twitter appeal by the anti-racist organisation SOS Racisme to post images of themselves or others wearing skimpy bathing costumes in public places, under the hashtag #jeportemonmaillotauparc (I wear my swimsuit in the park).

The five attackers, aged 16 to 24, were quickly arrested and the three oldest have been remanded to appear in court in September, while two girls aged 16 and 17 face further questioning. The authorities have not named them but said that they all came from housing estates with large Muslim populations.

It is not yet clear whether their unnamed 21-year-old victim was of French or north African origin. She was sunbathing with two friends in the Parc Léo Lagrange in Reims on Wednesday when one of the women verbally abused her for “immorally” exposing so much flesh in a public place. When she shouted back, the other girls and young women crowded around and slapped and punched her, police said. Passers-by intervened, and the victim was badly bruised rather than seriously hurt.

Police told L’Union newspaper that the victim was not able to say whether or not her assailants were motivated by “religious opinions”.

Arnaud Robinet, the mayor of Reims, said: “We have to be very careful not to jump to conclusions. All the same, I can understand why people have assumed that this attack had religious motives. If that turns out to be the case, it is a very serious incident.”