The announcement was part of a keynote speech outlining the new Socialist government's five-year plan.
"In the first half of 2013, the right to marriage and adoption will be open to all couples, without discrimination," Mr Ayrault told parliament.
"Our society is evolving, lifestyles and mentalities are changing. The government will respond to that."
The confirmation came just days after Paris held its annual Gay Pride parade, which this year was buoyed by the promise of the new government to legalise gay marriage and adoption rights.
A recent survey by pollster IFOP said that in France, gay people make up 6.5 per cent of the electorate, compared with practising Catholics at 4.5 per cent. A survey carried out at the beginning of the year also showed that 63% of French people are in favour of gay marriage while 56% support gay adoption.
A number of European nations including Germany, Sweden, Belgium, Spain, Sweden, Norway and Britain already allow gay adoption.