I'm in the middle of doing this exact job at the moment and have done a few before.
The concrete will not be deep and will have been laid over either stone flags or a wooden cradle. Best thing is to remove it totally with a chisel and hammer or your SDS on roto-stop etc.
Then, replace with wood, installing new joists if necessary to support the boards. Some people use a sheet of ply but I have actually knocked out the complete fireplace so I'm going to use matching floorboards (yes, you can always still get any size) and board right to the back of the fireplace.
Actually, of all the ones I've done before, this one looks the best. I have removed the plaster for about a foot all the way around the opening and then finished off the bricks so that the effect is that of framing the nice brick and recess, into which I will sit (for decoration only) an old enamel wood burning stove.
Hope that helps with regard to the floor. Let me know if you need more help but definitely remove that concrete which is proud of the rest of the floor.
Rob