It will. The problem is that MSFS likes an airplane to intercept a localiser as far from the airport as possible.
Accurate intercepts for ILS in this manner are also a part of real-life aviation.
To get a good ILS landing, ensure your frequency selection is correct, INS/RAD switch is set to RAD, and autopilot is engaged.
Intercept the ILS at a range of 15 nautical miles, and an altitude of 5,000ft, already facing the runway, on runway heading and at 250 knots or less.
Check that the ILS glideslope indicator, in the HSI, is detecting the glideslope.
Engage GLIDE button to set Concorde into AUTOLAND.
Concorde will settle into the approach and guide all the way in to land. This has been repeatedly tested and confirmed.
(NOTE: some airports in MSFS are misaligned with ILS. A small manual correction may be needed just prior to landing).