The results, if confirmed, amount to a clear defeat for Mr Hollande, just as his government was trying to push through economic reforms this year to capture early signs of recovery in Europe's second-largest economy.
Speaking on Sunday, Manuel Valls, the prime minister, acknowledged defeat. "It is incontestable," he said, blaming divisions in the left that he said had proved deadly.
Earlier this year, Mr Valls was forced to push one of the government's key economic reforms through parliament by decree as he headed off a possible revolt by far-left members of his Socialist party.
Mr Valls said Sunday's defeat would nonetheless do nothing to sway the government from its reformist path.
Jubilant, Mr Sarkozy said: "Announcing that the vote today would do nothing to change its policies, Hollande has deliberately chosen to ignore the message delivered by the French."
With Sunday's local election safely behind him, Mr Sarkozy will doubtless already be looking ahead to next year's UMP primary elections to choose a presidential candidate.
The former president, whom Mr Hollande beat in 2012, has yet to declare his intentions to return to the Elysée, although most political analysts take it as a given.