Mr Polanski, 76, is currently in custody in a Zurich prison.
The French-born Polish director was detained on Saturday as he arrived in Zurich to receive a lifetime achievement award.
"We're calling on every film-maker we can to help fix this terrible situation," Weinstein said.
A petition has been signed by film-makers and actors including Monica Bellucci and Fanny Ardant expressing dismay at Mr Polanski's arrest.
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.
And British novelist Robert Harris described the arrest as "disgusting treatment".
Mr Polanski is directing a film adaptation of his book The Ghost. Mr Harris said the production team were "reeling from the news".
Oscar-winning director Andrzej Wajda was among members of the Polish Filmmakers Association calling on their website for Switzerland to immediately release Mr Polanski and for the US to review his case.
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".
Los Angeles District Attorney Steve Cooley comments on Roman Polanski's arrest
Justice spokesman Guido Balmer said the difference with this particular trip was that authorities knew exactly when and where Mr Polanski would arrive. Switzerland does not perform passport checks on arrivals from 24 other European countries.
The Swiss Directors Association also criticised the arrest, describing it as "not only a grotesque farce of justice, but also an immense cultural scandal".
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".
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".
American 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.
A judge dismissed his bid to throw out the case earlier this year because he did not appear in person in court but said there was "substantial misconduct" in the handling of the original case.
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
The director is being held under a 2005 international alert issued by the US.
Sandi Gibbons, a spokeswoman for the Los Angeles County district attorney's office, confirmed that moves to detain the director were set in motion last week.
"It wasn't a big secret that he was going to be in Zurich. They had announced it on the internet," Ms Gibbons said.
There had been two previous attempts to arrest Mr Polanski when he planned visits to countries that have extradition agreements with the US, but each time he apparently learned of the plans and did not travel, Ms Gibbons said.
Mr Polanski was initially indicted on six counts and faced up to life in prison. He has not set foot in the US for more than 30 years.
The victim at the centre of the case, Samantha Geimer, has previously asked for the charges to be dropped. She has already sued Mr Polanski and reached an undisclosed settlement.
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