France joins the United States, Australia and a number of other countries now carrying out air raids in the country.
It is labelling the move self-defence, saying the strikes are intended to stop the militants from carrying out attacks in France.
French president Francois Hollande has spoken briefly to reporters at the United Nations in New York after the strikes were first announced in Paris.
The announcement came a day before he was scheduled to make a keynote address at the UN General Assembly.
President Hollande says more attacks are likely against IS, also known as ISIL and Daesh.
"Some of the strikes could take place in the coming weeks, if necessary, still with the same goal. It is about identifying targets that correspond to training centres or places where we are aware that the terrorist group Daesh is threatening the security, or could threaten the security, of our country or undertake some terror attacks."
Mr Hollande says the targets were identified in earlier reconnaissance flights and were destroyed without causing civilian casualties.
French fighter jets had already been targeting IS in Iraq as part of the US-led coalition.
But due to attacks inside France and the growing humanitarian crisis gripping Europe, the French president says there is little choice but to intervene and expand its air raids to Syria.
"I am here in New York, and, together with my minister of foreign affairs, I will be meeting with all of the partners and stakeholders on what is called the Syrian conflict, a conflict that has led to some 250,000 deaths and for which Bashar al-Assad is the main person responsible, even though now, and for the past few months, ISIL has been responsible for terrible atrocities. A political solution requires that all stakeholders are involved, without excluding anyone. That being said, France considers that the future of Syria cannot be with Bashar al-Assad."
France is also calling for a global solution to the Syrian crisis, saying it supports UN special envoy Staffan de Mistura's initiative to work towards a political transition for the country.
It comes amid a flurry of diplomacy over Syria's civil war, as heads of state gather for the General Assembly.
The United States has built its own coalition of mainly Sunni Arab and Western countries to fight IS in Iraq and Syria, but Russia is taking another path that includes President Assad.
US Secretary of State John Kerry began talks with his Russian counterpart, Sergei Lavrov, on the sidelines of the U-N meeting.
He has urged Russia not to go alone and says it is critical that all efforts are coordinated.
"We have concerns about how we're going to go forward, but that's precisely what we're meeting on to talk about now. Our presidents will be meeting tomorrow. This is the beginning of a genuine effort to see if there is a way to de-conflict, but also to find a way forward that will be effective in keeping a united, secular Syria that can be at peace and stable again without foreign troops present."
US president Barack Obama is meeting his Russian counterpart, Vladimir Putin, with Syria topping the agenda.
Russia has stepped up its military involvement in Syria in recent weeks, with US officials accusing it of sending combat aircraft, tanks and other equipment to help the Syrian army.
In an interview with US networks recorded ahead of the scheduled meeting with Mr Obama, Mr Putin warned against any attempts to overthrow the Assad government.
He says it could result in a failed state, like Iraq or Libya.
"There's no other solution to the Syria crisis than strengthening the effective government structures and rendering them help in fighting terrorism, but, at the same time, urging them to engage in positive dialogue with the rational opposition and conduct reform."
And international thinking could be shifting, with Australian foreign minister Julie Bishop indicating the Federal Government may engage with Syria's president.
Australia has long held the position that Bashar al-Assad must step aside as part of any durable peace settlement.
But the possible policy shift may acknowledge the Assad government could be critical in preventing further gains by IS.
Ms Bishop says all options should be on the table.
"That is realpolitik. That is being realistic. In 2011, there was a Geneva Process that set out what the coalition partners believed was achievable at that time. It hasn't achieved it. So, therefore, we should reconsider the position."
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