There is a group of European countries that gets uncomfortable every time France comes up with ideas to deepen ties with other euro economies.
Labeled the "Hanseatic League," this group includes the Netherlands, Finland, Denmark and Latvia. Its name refers to the confederation free-trading city states in the northern part of Europe that started in the 14th century.
The Hanseatic League has for about a year questioned France's determined efforts to strengthen the economic union through motions that include putting together a euro zone budget.
Instead, the group believes that each government needs to consider its own fiscal obligations and put the necessary policies in place — doing so would reduce efforts at the euro zone level to further deepen integration between the 19 countries.
"We are strongly in favor of euro zone reform. The question is what kind of reform," a European official, who is a member of the so-called league and who did not want to be named due to the sensitivity of the discussions, told CNBC.
Differing opinions on how to move forward within the euro zone are nothing new, of course. But they seemed to reach a new level last weekend when France's Finance Minister Bruno Le Maire publicly stated Paris' frustration with the group.
"Let's imagine that France tries to create a club of the southern countries with Portugal, Italy, Spain — what would be the reaction of the other member states? Do you think that it would be a positive one? Do you think it would improve the situation of Europe?," Le Maire told the Financial Times.
"I am not comfortable with the idea of creating new circles, new clubs, new leagues within Europe," he added.
His comments followed a meeting with his Dutch counterpart Wopke Hoekstra — often cited as the head of the Hanseatic League.
At the moment, France and the Netherlands are at loggerheads over a proposal to create a euro zone budget, a financial pot available only to the 19 countries that have adopted the euro and that will help them to absorb any economic shocks that may occur.
"It is not just a question of whether you want it or not. It is a far more complicated issue. You also have to ask for what purpose, how, who pays and who decides. It has to make sense and work in practice," the European official told CNBC.
Le Maire said at a press conference in Brussels last week that the aim is to have a euro zone budget in place in 2021. Despite support from Germany, there are open questions about how much money euro zone governments would have to put aside to finance such a budget.
Speaking at the same press conference, German Finance Minister Olaf Scholz said it was important to strengthen the euro zone now as it will be the most important engine growth of Europe when Brexit takes place.
"The euro zone will become even more important within the framework of the European Union. When the United Kingdom will have left the European Union, 85 percent of GDP (gross domestic product) will be produced in euro(s)," Sholz said.
France and Germany want to reach an agreement on the euro zone budget proposal next month.
The Hanseatic League "is a group of countries which tries to organize a counterweight to the Franco-German axis; a normal step as a single smaller country alone will hardly have its voice heard," Carsten Brzeski, chief economist at ING, told CNBC via email.
"The common denominator of the group is that hardly any further reforms of the monetary union are needed… a voice which many politicians in Berlin, by the way, do appreciate. It allows the German government to embrace French proposals, while at the same time provides enough counterweight not to go all the way," Brzeski said.
The European official who is a member of the Hanseatic League explained that, "At the moment, we are eight countries, we are open to others… but we also like to maintain some cohesion in the group.
"Our meetings are irregularly regular, usually every two months on the sidelines and after the Eurogroup (the official meeting between the 19 finance ministers of the euro zone), but sometimes for logistical reasons we have to reschedule."
Ricardo Garcia, chief euro zone economist at UBS, told CNBC that the current framework is unlikely to change significantly, meaning that whenever the next crisis hits, the euro zone will have to deal with it using current mechanisms, or create new ones then.
"Whatever we get (by) mid-December will be the response to Brexit for the time being, and what we'll have for the next downturn," he said in an email.
Euro zone reform is due to be discussed at a summit in Brussels in two weeks.