The 73-year-old leader has nine months left in office and his popularity is plummeting, but he has refused to rule out a third term.
He also won't publicly back the 2007 presidential bid of Interior Minister Nicolas Sarkozy or bow out of the race himself. Asked for an accounting of his 11-year tenure, Chirac said he had better things to do.
In a nationwide television interview during the garden party traditionally thrown by the presidential Elysee Palace on France's July 14 national day, Chirac said that he was still after results.
Hours earlier, he reviewed the soldiers, Foreign Legionnaires and even Paris firefighters who marched down the Champs-Elysees. Overhead, jets of the Patrol of France streaked blue, white and red colors of the French flag. Fighter jets, AWACS surveillance planes and helicopters took to the skies.
At the garden party, packed with some 5,000 guests, the focus was on politics, with Sarkozy supporters hoping for a blessing from Chirac that did not come.
However, the president had friendly words for the man who is expected to be officially named the candidate of Chirac's Union for a Popular Movement, or UMP, on Jan. 14.
"My relations with Nicolas Sarkozy are very good and pose no problems," Chirac said. He also said that UMP's designation of a presidential candidate "in no case" concerns him.
Chirac repeated he will announce his intentions in the first few months of 2007. No French president has served more than two terms in the Fifth Republic.
During the interview, Chirac listed reforms he still hopes to achieve, including bringing unemployment, currently at 9.1 percent, below 8 percent.
Sarkozy supporters were disappointed that Chirac withheld his own intentions, and his support for Sarkozy.
"Today, we are at the end of the (Chirac) era," said lawmaker Dominique Paille.
"It's like in a football match. You have to make the whole team understand that nothing is won or lost until the final whistle," said Azouz Begag, equal opportunities minister, defending Chirac.
Security was tight at the parade, with Metro stations in the area closed off and police stationed along the streets.
On July 14, 2002, a gunman tried to shoot Chirac during the Bastille Day parade. The president was unhurt, and the attempted assassin was sentenced to 10 years in prison.
Bastille Day commemorates the 1789 storming of the former Bastille prison in Paris by angry crowds, sparking the revolution that brought an end to the monarchy in France.