Branding Sharon's language "unacceptable", a French Foreign Ministry spokesman said on Sunday Paris had demanded an explanation.
France, home to western Europe's biggest Jewish and Muslim communities, has been troubled by attacks on Jewish people and property in recent years.
French media, in most cases, blamed some of the attacks on youths of North African origin angered by the Israeli-Palestinian conflict.
However, the French Muslim community has also been the target of racist, anti-Semitic attacks with Muslim youth harassed, mosques vandalised and Islamic burial grounds desecrated.
On 10 June, a French court convicted former sex symbol Bridget Bardot for inciting racial hatred in her new book, A Scream in Silence.
"Madame Bardot presents Muslims as barbaric and cruel invaders, responsible for terrorist acts and eager to dominate the French to the extent of wanting to exterminate them," the court said.
She was ordered to pay a fine of €5000 ($6000).
Sharon, who regularly calls on all the world's Jews to migrate to Israel, acknowledged in a speech to Jewish leaders in Jerusalem that the French government was making efforts to stem anti-Semitism.
But he claimed the threat was so grave that French Jews should head for Israel without delay.
"If I have to advise our brothers in France, I'll tell them one thing - move to Israel, as early as possible. I say that to Jews all around the world, but there [in France] I think it's a must and they have to move immediately," Sharon said.
The French spokesman said: "We have been informed of comments made today by Sharon calling on the Jews of France to emigrate to Israel.
"If I have to advise our brothers in France, I'll tell them one thing - move to Israel, as early as possible"
"We immediately made contact with the Israeli authorities to ask for an explanation of these unacceptable comments."
About 600,000 Jews and five million Muslims form part of France's population of 60 million.
The French Interior Ministry registered 67 attacks on Jews or their property and 160 threats against Jews in the first quarter of this year compared with 42 attacks and 191 threats in the last three months of 2003.
False anti-Semitic attack
On 15 July, French police said they had uncovered a lie perpetrated by a young woman, Marie LeBlanc, who claimed she was the victim of an anti-Jewish attack by six youths who looked North African.
LeBlanc had alleged that her attackers tore her clothes and painted a swastika on her stomach while she was travelling on a subway car.
LeBlanc's mother admitted her
daughter concocted the attack
At the time, newspapers said the woman - who is not Jewish - was targeted because she was suspected of living in a predominantly Jewish quarter and therefore presumed to be Jewish.
However, a police investigation turned up no witnesses and no sign of the six men on security video recordings.
Later on Tuesday, according to media reports, the woman retracted her accusations.
Her mother, like several other people who knew her, said she had a history of making up stories. Now, she could face up to six months in prison and more than $9000 in fines for her lies.