In the US and UK, for example, minute-long episodes drawn from Fox TV's 24 television series, were available during the show's last season.
There have been prizes for movies made on or for mobile phones at events such as the Sundance Festival in the United States.
However, the three-day event which starts on Friday at the Forum des Images film centre in Paris is the first in Europe dedicated to films made on phones, said Ms Herszberg.
A film festival in Taiwan for Asian directors of phone films began in late September.
Several months ago the Forum handed out 100 3G phones to film-makers, writers, musicians, and other creative types and told them to go off and experiment.
"Mobisode" clips were available during the last season of 24
They came back with films that spanned genres from film noir parody to personal diaries to a 90-minute feature entitled Jours où Je N'existe Pas (Days When I Don't Exist).
Fourteen of these films are in the running for prizes of cash and mobile phones, to be handed out Sunday at the close of the festival.
The festival is jointly sponsored by Nokia, the world's leading mobile phone maker, and the French mobile operator SFR.
They and other films will be shown on regular cinema screens in the Forum over the weekend, but can also be seen on mobile phone screens in installations in the centre's lobby.
Films being shown on these phone screens also include short films from the Lumière brothers, the French inventors whose 1895 film Workers Leaving the Lumière Factory is considered the first motion picture.
The festival director explained that the constraints of making movies on a mobile phone were in some ways similar to producing film on the primitive "cinematographe" camera invented by the Lumières.
The films on offer range from 30-second shorts to full-length features
She rejected suggestions that mobile phone films were merely a gimmick, pointing out that digital movie cameras were at first scorned by serious film-makers but have now been widely accepted.
Wladimir Anselme, one of the film-makers being showcased at the festival, agreed that the reduced capability of the mobile phone drove him to be more creative.
"Whatever tool you use gives you creativity, you have to overcome its limitations," said Anselme, who is also a musician and cabaret artist.
He made several films with his 3G phone, two of which were brief epsiodes in a film noir series and will be shown at the festival. He describes them as a witty parody mix of Martin Scorcese's Taxi Driver and early Jean-Luc Godard gangster movies.
Festival-goers keen to break into this new art form will be able to make their own mini-films in a special studio and editing facility set up in the Forum, where actors and technicians will be on hand to help.
And, this being France, the festival will also host several weighty round-table debates on subjects such as the meaning of the new art and its sociological implications.