French President François Hollande announced the news at a press conference in Paris on Tuesday.
He insisted that France will not intervene militarily but said it might review its refusal to arm rebel fighters.
“This question will have to be necessarily reviewed not only in France but in all countries which will recognise this government,” he said.
National Coalition chief Ahmed Moaz al-Khatib earlier urged world powers to arm groups fighting Syrian president Bashar al-Assad’s regime. He described Assad’s foes as desperately needing “specialised weapons” in order to “cut short the suffering of the Syrians and their bloodshed”.
The United States has called the coalition a “legitimate representative” of the Syrian people.
Britain has called for more evidence that the grouping has strong support inside Syria, before it joins France in recognising the new coalition.
France’s decision to recognise the SNC came shortly after six members of the Gulf Cooperation Council, Saudi Arabia, Bahrain, the United Arab Emirates Oman, Qatar and Kuwait, agreed to support it.
The groups involved in the coalition agreed on Sunday to unify their fighting forces under a supreme military council and set up a national judicial commission for the rebel-held areas in Syria.
They intend to form a provisional government once the coalition has obtained full international recognition.
EU foreign ministers meeting in Cairo on Tuesday welcomed the creation of the bloc, urging a stronger representation of those who oppose Assad’s regime.
The 22-member Arab League has stopped short of granting it full recognition, stating, however, that is considers it “the legitimate representative of the Syrian opposition”.