"On many principles we are quite close," the government source told journalists in Berlin.
"There is a chance to come to an agreement with the French on a fair system ... before the next environment council (meeting of EU environment ministers) at the beginning of June," the source added.
Germany, which produces bigger, more gas-guzzling vehicles than the smaller French versions, wants all types of cars to contribute to the overall reduction in emissions, the German source said.
Berlin has become a strong critic of the European Commission's plans presented last December, which foresee the biggest emissions reductions coming from the biggest emitters, a stance which it deems will penalise its automobile industry.
Brussels has proposed that all cars sold in Europe in 2012, whether European-made or not, should reach an overall objective of 120-130 grams of CO2 emitted per kilometre, as opposed to an average of 160 grams today.
The EU executive wants to penalise automakers which do not reach the goal by 2012 with a charge of €20 ($32) per extra gram of CO2 per car, with the penalties rising to €95 ($152) by 2015.
Each manufacturer must attain the average emissions target, and that's where the Germans feel they are being unfairly targeted, as their industry would have to make greater strides than the French or the Italians in order to comply.
According to the German government source the discussions with Paris - involving the economic and environment ministers as well as German Chancellor Angela Merkel's office - are notably about the 'curve' of the graph, how everyone's contribution to the target is defined.
Germany does not contest the idea of progressive fines from 2012, the source explained, however their gradation is under debate. The penalties might also be applied only to certain models initially, she added.
A Franco-German agreement would be a prelude to a wider deal between the 27 EU member states, which European leaders have promised to reach this year.
The car emissions objective is seen as testing the EU's determination to reach the wider goal of reducing greenhouse gas emissions by 20 percent by 2020.
France, which will assume the EU's rotating presidency from Slovenia in July, has promised to do all in its power to reach agreement.
Following Silvio Berlusconi recent victory in Italy's general election, the Italians, also makers of smaller cars, are set to join the debate with the French and Germans, the government source in Berlin said.
Berlin and Paris have to "bring the interests of the Italian car industry into the debate otherwise we are not going to reach an agreement," she said.