The country had announced earlier this month that it would expand its aerial campaign
against ISIS in Iraq -- which it began a year ago -- to include the militant group's positions in Syria.
The French president's office said that the strikes in Syria, which began Sunday, were based on intelligence gathered from air surveillance operations conducted over Syria during the past two weeks.
"Our country confirms its firm commitment to the fight against the terrorist threat Daesh," the statement said, using the Arabic acronym for ISIS. "We will strike whenever our national security is at stake."
President Francois Hollande, speaking on the sidelines of the U.N. General Assembly in New York, described the camp as a "threat to our country."
"We reached our goal and the whole training camp was destroyed," Hollande said.
Six aircraft were used in the mission, which was led by the French but closely coordinated with the U.S.-led coalition, he said.
Despite the "horrible acts" committed by ISIS, Hollande placed the blame for the Syrian crisis on the country's long time strongman Bashar al-Assad.
"Bashar al Assad is the main person at fault, although Daesh commits horrible acts," Hollande said. "The future of Syria cannot happen with Bashar al Assad."
String of terrorist attacks
France has been the site of a number of terrorist attacks this year.
Islamic extremists killed 17 people in a quick succession of attacks in Paris in January
, including the shooting deaths of staff members in the offices of the satirical magazine Charlie Hebdo.
In June, authorities said a man in southeastern France decapitated his boss
, displayed the severed head with Islamist banners and also set off an explosion in a factory. And last month, three American men brought down a suspected terrorist gunman
who tried to open fire on a train bound for France.
But France has also linked the refugee crisis Europe is facing in part to ISIS, saying it would strike the group for driving thousands of civilians out of Syria. "We're not going to receive 4 to 5 million Syrians, so the problem has to be dealt with at source," French Prime Minister Manuel Valls told CNN's Christiane Amanpour.
France has been in talks with Russia about a political solution in Syria.
"Russia supports the regime of Bashar (al) Assad. But it also wants to find a political solution. And anyway, there will not be any political solution without a dialogue with all of the parties who directly or indirectly are involved with Syria," Valls said.
France also planned to hold talks about Syria with Iranian President Hassan Rouhani.