Markets have been on the edge regarding Italy's future spending, but there are other countries challenging European fiscal rules.

France, the second-largest economy in Europe, received a letter from Brussels last week, warning that its planned debt reduction in 2019 does not respect the proposals that Paris had agreed previously with the EU. Spain, Belgium, Portugal and Slovenia were also effectively told off by the EU.

In the case of France, the 2019 budget plan sees its structural deficit (the difference between spending and revenues, excluding one-off items) falling 0.1 percent this year and 0.3 percent in 2019. Paris had agreed in April to an annual reduction of 0.6 percent of GDP (gross domestic product) for its structural deficit.

Though the tone of the warning from Brussels to Paris was softer than the tone towards Rome, the two countries have perhaps more similarities than differences.

The French 2019 budget "shows that the government relies heavily on very optimistic revenues to achieve fiscal consolidation and that spending is out of control again," Daniel Lacalle, chief economist and investment officer at Tressis Gestion, told CNBC via email.

Italy has also been criticized for having very upbeat economic forecasts in its 2019 budget plan.

"In the case of France, it is a very difficult budget to accept by the European Commission because France has not had a balanced budget since 1974 and has missed its own deficit targets more than eleven times," Lacalle added.

Data from the European statistics agency, Eurostat, shows that since it started collecting French data in 1978, France has never registered a budget surplus. Italy, which has provided data since 1995, has also never presented a budget surplus.