The European Commission has said it is likely to approve France and Italy's 2015 budgets after both countries made adjustments to their first proposals, submitted earlier this month.
France had initially disregarded the Commission's calls for further budgetary cuts.
Since the financial crisis, the Commission has gained greater powers to ensure members meet deficit targets.
France's original budget forecast a deficit of 4.3%, above the 3% target.
The 3% target would not have been met until 2017, under this first proposal.
The budget deficit is the amount a government spends over and above its annual income, expressed as a percentage of total economic output, or GDP.
"After taking into account all of the further information and improvements... I cannot immediately identify cases of particularly serious non-compliance which would oblige us [to reject the plans]", said EU Economic Affairs Commissioner Jyrki Katainen.
France and Italy have been negotiating with the Commission since they submitted their budgets on 15 October.
On Tuesday, France's Finance Minister Michel Sapin said he would cut a further €3.6-3.7bn ($4.6bn; £2.8bn) from the 2015 budget to meet the EU rules.
He said he had found the money because of lower-than-expected costs on interest payments, as well as lower contributions to the EU's budget.