generally your space is well distributed.
However as an interior architect some changes are to be made in order to have an optimized space.
For this I defined the general part in 3 parts, add walls would only reduce your space and you lose a lot of luminosity.
To delineate the parts without partition, several solutions have been made. I just add a false ceiling in the kitchen in order to have a more intimate corner, playing on volumes, false ceiling ends with the return of the chimney. In front, I added new volumes coming create a visual separation between the dining room and living room. These volumes allow you to have more storage space for both you and for your children. The luminosity is an important point in your project (the photos attests) to fix it, I played with colors, as in the kitchen with its stainless steel coating which will reflect the light in your room. Color chairs bring you bright, modern contrast. Your flooring is very beautiful, I liked to keep him but I chose another more light wooden floors with wider slats. (which comes blur the height of your ceiling.)
In a project such as your lighting is very important in order to have more natural light , you should opt for a more modern stairs or steps are visible to let the light .
Recently, you spoke of a space or the children of your game mayest not knowing the age of your children , it is difficult to dedicate a defined space, more would be a bad choice because your children will grow up and have to other activities . The creation of the volume on the brick wall will allow your children to play and store are many games .
In conclusion, I am convinced that your ground floor needed a facelift and some tips to improve development in place.