A team of 15 detectives, backed by uniformed officers carrying photographs of the girls, is combing the West End in the hope of finding them.
Anjelique's father, Noel Wozniak, 45, said it was out of character for the girls to go off on their own. They were unused to big cities and had rarely been away from their home village of Grenay, near Lille.
Jacky Ranson, 49, father of 16-year-old Laetitia, told a news conference at Scotland Yard: "We would like anyone to get in touch with the police and we appeal to our daughters, if they are safe, to go to any policeman or place of safety. We just want to know they are all right."
Mr Wozniak added: "We think maybe they have been kidnapped. Something bad must have happened to them."
The girls were last seen at 4pm on Wednesday at Selfridges in Oxford Street. Detectives are studying closed circuit television videos from the store and nearby premises in the hope of spotting them. Detective Inspector Rick Turner, leading the police team, said: "The longer this goes on the worse it looks but at this stage we have no evidence to suggest they have been kidnapped."
He added: "We have no idea where they [the girls] could have gone. They appear to be nice young girls who have apparently acted out of character."
Both girls are 5ft 2in, and heavily built. Anjelique was wearing glasses and distinctive yellow Dr Marten boots. Laetitia was wearing a black jacket and blue jeans.
Anyone with information is asked to telephone police on 0181 246 0776.