The European Commission is keeping up the pressure two days after it extended the deadline for France, the eurozone's second biggest economy after Germany, to get back below the EU's ceiling of 3.0 percent of economic output.
Brussels said France must use the extra breathing room to reach a deficit of 4.0 percent of annual economic output in 2015, 3.4 percent in 2016 and 2.8 percent in 2017.
The first two years are tougher than France's own targets of 4.1 percent in 2015 and 3.6 percent in 2016.
French Finance Minister Michel Sapin, speaking during a visit to Slovenia, said the country would be able to meet what he described as "demanding" but realistic targets.
The EU had disappointed fiscal hardliners when it said Wednesday that France would escape possible fines for now and get two more years to get its house in order, while Italy and Belgium were let off the hook completely.
But to reach the EU's new benchmarks France will have to find additional savings in an economy growing very slowly, putting the government on the spot as it tries to boost growth through increased public spending.
For 2015, the Commission, the EU's executive arm, estimated the savings required at 0.5 percent of GDP, up from the current 0.3 percent -- that means additional savings worth at least 4.0 billion euros ($4.5 billion).
But for 2016, Paris must find an even tougher 0.8 percent and then 0.9 percent in 2017, the Commission said in a series of recommendations following Wednesday's deadline extension.
The EU looks at the deficit -- the difference between spending and revenue -- in central and local government spending plus social welfare systems.
"France should step up efforts to identify savings opportunities across all sub-sectors of general government, including at social security and local government level and use all windfall gains for deficit reduction," it said in a statement.
France, like many of the European Union's 28 member states, has been in breach of the deficit limit for years and has won two previous deadline extensions.
But new rules imposed by Brussels to tame the eurozone debt crisis since its height in 2010-2012 has given the Commission much greater oversight of national budgets.
At the same time, Germany, the bloc's paymaster and determined austerity advocate, insists the budget rules must be met if the EU is to achieve sustainable growth.
Berlin has been reluctant to cede any ground to France and Italy over their demands that austerity be eased at least slightly to give them more leeway to boost growth.