The campaign aired for the first time this week, to coincide with London Fashion Week, but has already outraged viewers.
According to an ASA spokeswoman: "A lot of the complaints are about the violence but some are concerned about the sexual content, which refers to the lesbian kiss.
"Some are also complaining that it has been created just to shock and they feel that is a problem."
She added that the ASA will be monitoring the ad and complaints over the next week before deciding whether to investigate.
The ad is part of a £2m campaign by Beattie McGuiness Bungay for French Connection's spring and summer collection.
It is directed by David Bowie's son Duncan Jones in the style of martial arts movies such as 'Kill Bill', under the slogan "fashion versus style". The fight includes a headbutt and clothes being ripped off, as well as the kiss.
This is just the latest run-in French Connection has had with the ASA, which put a pre-vetting order on the company's outdoor ads and posters because of the use of its controversial FCUK slogan.
French Connection has since ditched the slogan from its advertising and marketing but continues to use it in-store and on clothing.
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