Contrails have nothing with speed to do. It's only a question about humidity. Every pound of fuel burned produces 1.2 pounds of water vapor which may freeze to ice particles - contrails, or evaporate depending on the conditions, ambient humidity and temperature.
But the Concorde cruises in the strotosphere where the air is much dryer, and it will normally not produce contrails up there.
At lower levels, however, it is no different than other airliners. Except that it consumes so much more fuel, and therefore produces more water vapor, and generally thicker contrails.
Regards, Preben Norholm
Always keep your number of landings equal to your number of take-offs