The Rolls-Royce/SNECMA Olympus 593 (which powered the Concorde) used a complex intake-ramp system to improve the engine's efficiency and prevent an engine shutdown or failure during supersonic flight from tearing the aircraft apart; it did the latter by dumping almost all of the intake air overboard via a set of spill doors, allowing it to bypass the inoperative engine and thereby avoid the considerable drag generated therein.
On the other hand, a windmilling engine restart (one of only two midair relight methods possible for the Concorde, as it had no APU - the other being the use of bleed air from a still-operating engine - and the only one available in the event of a quadruple engine failure)1 requires that ambient air be forced through the engine in order to get it spinning, which would seem to necessitate closing the spill doors and not dumping the intake air overboard.
Could the Concorde's engines have been windmill-lit during supersonic flight, or would the aircraft have had to have been slowed to subsonic speeds prior to attempting a windmill restart?
1: While admittedly an unlikely scenario, there are multiple possible ways for this to happen other than fuel exhaustion; possible examples would be if a Concorde inadvertently flew through a volcanic ash cloud, or suffered fuel contamination, or experienced an upset at high altitude.