Tuesday's motion is the first step in his legal battle to avoid extradition to the US, which issued his arrest warrant.
Polanski, who was arrested at the Zurich film festival on Saturday, is currently in a Zurich cell where he receives three meals a day and is allowed outside for an hour of daily exercise.
On Monday, Bernard Kouchner, the French foreign minister, and Radek Sikorski, his Polish counterpart, urged Switzerland to release the film director.
The pair also petitioned Hillary Clinton, the US secretary of state, over the matter.
Frederic Mitterrand, the French culture minister, said Polanski had been "thrown to the lions".
"In the same way that there is a generous America that we like, there is also a scary America that has just shown its face," he said.
Samantha Geimer, the victim, who previously sued Polanski and reached an undisclosed settlement, has since joined his bid for the case to be dismissed.
|Polanski won best director for his film The Pianist in 2003 [AFP]
But Polanski is considered by the US authorities as a fugitive. Since fleeing the US, he has lived in France avoiding countries that have extradition treaties with the US.
Polanski's life has often featured in the media, first after the murder of Sharon Tate, his pregnant wife, by the Charles Manson cult in 1969.
A native of France who was taken to Poland by his parents, Polanski escaped Krakow's Jewish ghetto as a child and lived off the charity of strangers. His mother died at the Auschwitz Nazi death camp in the 1940s.
He worked his way into film-making in Poland, gaining an Oscar nomination for best foreign-language film in 1964 for Knife in the Water.
Offered entry to Hollywood, he directed Rosemary's Baby in 1968 and went on to make another classic, Chinatown, released in 1974.
In 2003, he won the Best Director Oscar for The Pianist.