Mr Polanski is currently in custody in a Zurich prison.
The director - who holds dual French-Polish citizenship - was detained on Saturday as he arrived in Zurich to receive a lifetime achievement award.
A petition has been signed by film-makers and actors including Monica Bellucci and Fanny Ardant expressing dismay at Mr Polanski's arrest.
Other Hollywood luminaries, including film producer Harvey Weinstein, have called for Mr Polanski's release.
French culture minister Frederic Mitterrand said President Sarkozy was following the case "with great attention".
Mr Mitterrand also told France-Inter radio that he and the Polish Foreign Minister Radek Sikorski have written to US Secretary of State Hillary Clinton, and said there could be a decision as early as Monday if a Swiss court accepts bail.
Mr Polanski has also been visited in prison by French and Polish diplomats.
French Consul General Jean-Luc Faure-Tournaire said the director "thanks the many people who have shown support". Poland's ambassador to Switzerland, Jaroslaw Starzyk, said Mr Polanski was "in good condition".
Mr Polanski's agent, Jeff Berg, told BBC Radio 4's Today programme the arrest was "surprising because Roman for the last 12, 15 years has lived in Switzerland, he has a home, he travels there, he works there".
Justice spokesman Guido Balmer said the difference with this particular trip was that authorities knew exactly when and where Mr Polanski would arrive.
Swiss Justice Minister Eveline Widmer-Schlumpf said that because of agreements with the US, "when Mr Polanski arrived we had no choice from a legal point of view but to arrest him".
Los Angeles District Attorney Steve Cooley comments on Roman Polanski's arrest
The Swiss media has rounded on the authorities.
"Switzerland let a guest walk into a nasty trap. We should be ashamed," said tabloid newspaper Blick.
Daily paper Le Temps said Switzerland had "shocked film buffs and friends of the arts with its kindly and efficient co-operation with US justice. It has angered Poland and France".
US authorities have up to 60 days to make a formal extradition request but Mr Polanski could then appeal to the Swiss courts.
In recent years, the director has asked a US appeals court in California to overturn a judge's refusal to throw out his case. He claimed misconduct by the judge, now deceased, who had arranged a plea bargain and then reneged on it.
1977 - Mr Polanski admits unlawful sex with Samantha Geimer, 13, in Los Angeles
1978 - flees to Britain after US arrest warrant is issued
1978 - immediately moves to France where he holds citizenship
1978 - settles in France, where he is protected by France's limited extradition with US
2008 - Mr Polanski's lawyer demands case be dismissed and hearing moved out of LA court
2009 - Mr Polanski's request to have hearing outside LA is denied
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