This youtube video partially attributes the retirement of all concorde fleets to the airfrance flight 4590 crash:Were the factors in this accident due to the concorde's design? Specifically, the tires of the concorde?
In short: No, the crash of 4590 could happen to other aircraft in the same situation: i.e. a blown out tire, a tank fire, subsequent structural issues, and at least two engines (of 4) not running properly.
The accident was due to the following causes:
• High-speed passage of a tyre over a part lost by an aircraft that had taken off five minutes earlier and the destruction of the tyre.
• The ripping out of a large piece of tank in a complex process of transmission of the energy produced by the impact of a piece of tyre at another point on the tank, this transmission associating deformation of the tank skin and the movement of the fuel, with perhaps the contributory effect of other more minor shocks and /or a hydrodynamic pressure surge.
• Ignition of the leaking fuel by an electric arc in the landing gear bay or through contact with the hot parts of the engine with forward propagation of the flame causing a very large fire under the aircraft’s wing and severe loss of thrust on engine 2 then engine 1.
None of these are related to the design or construction of the airframe itself. This podcast with one of the pilots also touches upon the accident and is perhaps one of the best primary sources of Concorde info.