"We have made progress but a fair bit of work remains to be done," Fabius said Wednesday after "a long night" of talks.
"On several topics we are almost at the end of our efforts thanks to the commitment of the parties," he told the conference at Le Bourget, near Paris, but he warned there were "still too many" undecided sections.
The draft has been reduced from 43 to 29 pages with three-quarters of disputed questions deleted, according to the French foreign affairs minister.
Disagreement has centred on how to finance the cost to developing countries of reducing greenhouse gas emissions, what target to set for the limit on global warming and how the burden will be shared between rich and poor countries.
Campaigning groups said they were concerned that too many compromises might be made in an effort to reach the deadline.