Solid wall with internal insulation is a really bad idea. It’s not thick enough to prevent damp coming through and or you may get condensation in the wall depth.
1m wide by two high is really small. If it’s in block you wil need 2 leaves with wall ties between the leaves and back to the existing wall. You will need to put Dpm between the leaves at the door junction or the damp will jump the gap. If you only have a 50mm cavity there’s no room for insulation.
I would do a 100mm timber inner leaf fixed back to the brickwork. Face in 9mm min osb/ply. Face with a breather membrane (tyvek) then build a wall in 100mm block. Remove circa 300mm external render, metal lath the joint then put render over. It may still crack but less likely, or just put a mastic joint there.
Internally insulate between the timbers, then finish with a foil backed plasterboard.
Or just get a blank door panel beside the French door to make up the width….