Polemic: Can we have two bakeries side by side?

In Clermont, Oise, two bakeries are standing side by side, glued on the same sidewalk. One has been there for eight years, and the other opened two days ago. The first baker is worried and angry, he knows that he will lose part of his turnover. In the shop next door, we want to calm the game. On the spot, this makes a lot of reaction. What are the rules in this kind of case? Could the mayor do something? (Conso and trends).