> However, why wouldn't it work to apply a fillet function
> on the edges I've selected ? (as seen on the screenshoot)

In your last screenshot you mean?

For the model that looks like this? :



That one has a problem with the curved surface, in this area:



If you go in there and move some control points around you can see that the surface actually folds back over top of itself:





If you use that boolean technique that I wrote about, it will make a better model, and then every other edge in there should fillet, except not all 3 of them going into that one particular corner.

- Michael