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.