Yes, the Concorde got airborne, and rose to some 200 feet. But I find it hard to dismiss the overweight problem and the missing spacer.
The higher the weight, the longer the takeoff run. Similarly, the missing spacer may well have slowed the acceleration of the aircraft, if not before the puncture, definitely after it.
Keep everything else the same and give Marty some extra speed when he pulled the Concorde off the ground (to avoid hitting the 747), and he would have had more options. Maybe he might even have made that tantalizingly close Bourget runway.
That ignoring the change in wind direction had no effect on the crash is illogical on the face of it. Had the Concorde switched runway, how likely is it that it would still have hit the metal FOD and burst a tyre?
I can accept that, as the BEA concluded, the tyre failure and subsequent fuel leak and fire were likely the primary causes of the crash. Not listing many of the other items pointed out in this thread and previous ones as at least contributory causes seems wrong, to me. And dangerous, in that it means little is likely to be done to address these problems.