Most of the info has already been given above.
I would add that on the TGV Mediterranee line there is a section of the line with a 320 km/h max speed, used by trainsets authorized to this speed (TGV Reseau, TGV Duplex). This has been done, in preparation for the TGV East-European commissioning, to gather information on possible differences between 300 and 320 day to day operations, especially regarding infrastructure maintenance (as French railways noticed important changes when increasing the max speed from 270 (TGV South-East) to 300 (TGV Atlantique).
Originally Posted by Track
The ICE-3 (not souped-up) has been tested up to 368 km/h and a souped-up TGV at a higher speed, but it did so much damage to the tracks and wires that no further tests were carried out.
Track: the “souped-up” TGV reached 515,3 km/h, as it has been mentioned above. But I am not aware of “much damage to the tracks and wires” due to this test. At the time it was even mentioned that there were no damage to infrastructure, contrary to what happened with the 1955 test (331 km/h with a conventional train). Do you have particular info about what you mention ?