The French Council of the Muslim Faith described the defilement of the mosque in the town of Montauban as "a racist and xenophobic provocation" and urged the authorities to bring those responsible to justice swiftly.
Pigs are considered unclean by Muslims, who are currently observing the holy month of Ramadan.
France's Union of Jewish Students said it was appalled by an incident that had occurred in a "worrying climate of hatred".
It was the first such incident in the southern Tarn-et-Garonne region, leading to speculation that it was a response to the March shooting spree of self-styled Al-Qaeda gunman Mohamed Merah.
Merah killed two paratroopers in Montauban, as well as three Jewish schoolchildren, a rabbi and another soldier in nearby Toulouse, before being killed himself in a police siege of his apartment.
The pig heads were hung on a gate at the entrance to the mosque shortly before morning prayers and a large amount of pig blood was spilled on the ground.
"It is contemptible," said the mosque's president, Hajii Mohamed. "To attack a religion like this, I don't know what is happening. People lose their heads, especially during Ramadan."
Interior Minister Manuel Valls condemned the act in a letter to Mohamed. "I can only be outraged in the face of such a revolting act that strikes a blow to the dignity of the Muslims of France," the letter said, adding that police were "completely determined" to bring the culprits to justice.
Abdallah Zekri, the chairman of France's Islamophobia Observatory, said Wednesday's outrage occurred against a background of an increase in anti-Muslim actions in the first half of this year.
"For this to occur during the holy month of Ramadan, it's unspeakable," he said. "It is racist provocation."
And the Representative Council of Jewish Institutions of France said it was "outraged by the hateful desecration of the mosque".
France is home to at least four million Muslims, the largest Islamic community in Europe.