That seems reasonable that Concorde would have a lower CL than a Cessna (as long as its incompressible flow, i.e. takeoff/landing speeds).
I believe a small CL is the reason for the relatively high speeds and angles of attack used by the plane.
Consider a general equation for lift:
L=(dynamic pressure, q)(CL)(AOA, alpha)(wing planform area, S)
In most cases, S is a fixed value. Things that change this value can be Fowler flaps or variable geometry wings.
For this case, we're also going to fix L, the lifting force.
That leaves us with CL, alpha, and q. If CL, a constant, is small, then we have to increase alpha and/or q.
On approach, Concorde will fly around 150% of the typical values of AOA and airspeed for a subsonic transport. This leads me to assume that the ship has a relatively small CL.
Also, to develop lift with a delta wing (vortex lift), some AOA is always necessary. Otherwise, you'll likely have equal pressures on the top and bottom of the wing as there's not much camber to cause circulation.
Hope that helps.
(OK experts, I gave you the target, fire away.)