The National Housing Information Agency (ANIL) has prepared and published a scatter map of rental housing prices. It affects exclusively the private rental sector. Municipal real estate is not included in the statistics - it is subject to its own rules, which do not always correlate with the market movements.
Usually as housing gets closer to the capital's borders, the prices for both apartments and houses rise. This is clearly seen in the color on the map itself.
For example, renting an apartment in Thionville will cost 13 euros per m². For houses it's 11.6 euros per m². As you approach the border, prices rise proportionally. In Mondorf, the they go up to 13.8 and 11.9 euros, respectively.
However, the rule “the farther from Luxembourg, the cheaper” does not always work. Do not forget about the regional features of France. In addition, life in large cities or key transportation points will always be expensive.