What does rain have to do with your cues if they are stored inside your home???
Is the home naturally aspirated...meaning outside air is same as inside air?
Is there air conditioning in your home?
The problem is likely that the humidity levels are too high in the home, the case gets warm and humid, then at night when the air cools, it leaves behind the moisture,...because the cool air can't hold the humidity so it sweats the moisture on the objects and in the objects that were warm and humid...
If its as I suspect...and the temperature in your home is going up and down with the weather...you are going to need to keep your cues OUT OF THE CASE...as the case will prevent the air flow from drying the cues...and it will actually trap in moisture...at the very least...leave the case open
I don't know about France but in Germany many homes have no air conditioning. They rely on fans.
My shop also has no air conditioning and when it's very humid I make sure that the fans are blowing on the leather to prevent mold from forming.
I do agree that whatever moisture is in a container will stay inside the container relative to the amount that the container is sealed. And conversely the moisture allowed into the container is also relative to the barrier.
I do not agree however that the moisture presence is a problem unless it's also so high that it's soaking other things. For example in our building in spring the moisture level is so high that the floors and walls remain moist. If I leave my windows open then my apartment gets just as clammy unless I run the fans and then it dries out somewhat. If this is not the case in the house in general then it's more likely that the particular cue is simply sucking up excess moisture.
I keep my cues, about 20 of them, in cases and in a display cabinet. I have not noticed any differences in the dryness level of any of them regardless of whether they are stored in cases or in the cabinet. My cases range from a fairly well sealed, but not airtight, GTF and JB tube cases to cloth soft cases lined with faux fur.
This is always an interesting topic. I wish I had time to run some experiments. I think one thing that people can do is read about how others handle their wooden instruments. I have seen cases with built in humidifiers and heaters to regulate the amount of moisture inside the case.
In the past I found a lot of interesting reading on the subject through Google.