If it were mine I would probably either move the cooktop and hood over or put the fridge there, or beside the sink as you mentioned. The sink side is nice because if you have groceries you can plop them on the island and go to the new pantry closet or to the fridge. Of course you can do the same with it on the other side of the range.
Not sure I understand what you mean here?
I would think about either shifting the cooktop to the left or move the fridge there. The problem with the fridge there is now the fridge will become a focal point.
There is something right beside your panty cabinet on the wall. It may be an outlet or a switch or a piece of molding, but there is something.
I'd put a flush mount in your ceiling medallion. Or a fixture coming out of it with lights which could be positioned to illuminate the island.
Pot racks look neat, but tend to block views and will become the focal point. I have ok pots, but really don't want to put them on display.
Another neat thing we did was to not have a knife block, we have a knife drawer with inserts. It has worked out awesome. I put my high end knives to the left, our crap knives in the middle and our decent knives to the right.
48" of space is quite a bit. We have 3' on one side and a little less on the other, but I did not secure our island to the floor so if I need to move it over I can. Our island is 3' x 6' in the cabinets.
I thought about concrete countertops, but they are not especially cheap when you consider everything. Granite has come down in price in the US to the point it hardly makes sense to do any other surface so long as you pick a lower cost rock. I wanted Quartz and it was more than granite. I also wanted Cherry cabinets and they were so expensive I almost fell over. We splurged on the finish of the island. Painted and antiqued was quite a bit more than stained.
Since you have no outlets you might consider putting in plugmold. You could do that on two walls undercabinet for an affordable cost. In our kitchen there was so much required it wasn't practical. To cut the plugmold to length you can take out the wiring and then use a wood chop saw if you have a good blade. Rewiring the plugmold is the most irritating task ever. If I was an electrician and a homeowner asked me for it I would charge out the wazoo because of how difficult it is to handle.
We did drawers on one large cabinet in the island for pots and pand, but have three with a fixed shelf and a roll out shelf at the bottom. Drawers would not hold things like a mixer and blender upright.
We also did every drawer and door with a soft close. The doors are simple and you can do them yourself, although I let our guy install them. The drawers are a mechanism and you will probably have to buy your cabinets with them.
What really will dress up the look is molding and light rail as well as a side panel on any exposed side surface. I don't know how you do cabinets in France, but I'd suggest looking at several places from custom to big box and see what the options are for them. We used a local company and they sold cabinets made in TX, and then they contracted our installer as part of the price. The nice part about that is I did not have to think about all the moldings. We went back and forth on design and features and then our installer helped with a few changes on the fly.