Francois Hollande said a military strike within days could not be ruled out.
US Defense Secretary Chuck Hagel said after the UK vote that Washington would continue to seek a coalition.
The UN is investigating claims that the Syrian forces of President Bashar al-Assad used chemical weapons. Bashar al-Assad denies the claims, blaming rebels.
UN chemical weapons inspectors visited a hospital in a government-controlled area of Damascus on Friday.
They are due to give their preliminary findings to UN Secretary General Ban Ki-moon over the weekend.
Francois Hollande told Le Monde newspaper that the UK vote, in which parliament rejected a government motion supporting the principle of military action, made no difference to France’s position.
“Each country is sovereign to participate or not in an operation. That is valid for Britain as it is for France,” he said.
He said that if the UN Security Council was unable to act, a coalition would form including the Arab League and European countries.
“But there are few countries which can have the capacity of enforcing any sanction through the appropriate measures,” he said.
“France will be part of it. France is ready.”
Francois Hollande ruled out strikes while the UN inspectors were in Syria. However he did not rule out the possibility that military action could be taken before next Wednesday, when the French parliament is due to debate the issue.
Neither France nor the US need parliamentary approval for action, and Secretary of State John Kerry said the US could not be held to the foreign policy of others.
The UK vote was welcomed in Russia, Syria’s main international ally.
Moscow said it reflected a growing public understanding of the dangers of an attack.
Syrian MPs are also delighted with the UK vote.
They believe a letter they sent to the UK parliament inviting their British counterparts to inspect the evidence of chemical attacks had helped sway the vote against military action.
China, which has vetoed previous UN Security Council resolutions against Syria, reiterated on Friday that no action should be taken until the UN inspectors have reported on their findings.
And Germany said of military action that “such participation has not been sought nor is it being considered”.
Officials in the US and UK had been insistent throughout the week that the Assad regime had carried out a poison-gas attack in eastern Damascus on August 21 in which hundreds were killed.
However, British PM David Cameron told parliament on Thursday he could not be 100% sure.
In the US, government officials briefed a Congressional committee on the case for launching action against Bashar al-Assad’s forces.
Eliot Engel, the top Democratic member on the House Foreign Affairs Committee, told reporters after the briefing that officials had said it was “beyond a doubt that chemical weapons were used, and used intentionally by the Assad regime”.
He said officials had cited evidence including “intercepted communications from high-level Syrian officials”.
Reports in the US media this week described Syrian officials suggesting in phone conversations that the chemical weapons attack had been more devastating than was intended.
More than 100,000 people are estimated to have died since the conflict erupted in Syria in March 2011, and the conflict has produced at least 1.7 million refugees.
Forces which could be used against Syria:
• Four US destroyers – USS Gravely, USS Ramage, USS Barry and USS Mahan – are in the eastern Mediterranean, equipped with cruise missiles. The missiles can also be fired from submarines, but the US Navy does not reveal their locations
• Airbases at Incirlik and Izmir in Turkey, and in Jordan, could be used to carry out strikes
• Two aircraft carriers – USS Nimitz and USS Harry S Truman are in the wider region
• French aircraft carrierCharles de Gaulle is currently in Toulon in the western Mediterranean
• French Raffale and Mirage aircraft can also operate from Al-Dhahra airbase in the UAE
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