I don't think it's the fastest, but I can tell you that the bullet train in Japan reaches speeds of 300 km/h if that helps! lol Now you have me interested and I wanna find out :)

Not as fast as it was when Concorde was flying. About 580 mph.

All current commercial transports are limited to the same speed of about Mach 0.92, because above that speed speed-of-sound effects start requiring design changes. Apart from Concorde, I believe the Convair 990 could do Mach 0.95, but I doubt that there are any of those left in service.

One of the trains( the name of which I don't remember) in france, has recently clocked the fastest speed of 596 km/h( thats for ground transport)

The fastest form of commercial passenger transport is jet aircraft travel, plain and simple. There are some fast trains and speedy boats but if you factor it out your much better off in a commercial jet, not to mention much safer. Today's age of commercial jets all are capable of cruising in the same range, anywhere from 430-510 knots. While there are a few business jets, such as the Citation X or the Gulfstream G-V that reach speeds a little higher, you cannot be sure the jet you are on is cruising any faster than a different model. Remember, cruise speeds for commercial jets are assigned by folks in offices miles away from the airport. The pilots may change or adjust accordingly if needed but it is not their job to determine economy as much as it is to manage the flight effectively according to procedure. The 747 you are taking across the Atlantic may be flying faster than the 777 behind it while the A340 to the East might be in the middle of the two. The next flight may be completely different. Half of the problems of speed in commercial airlines involve congestion of skies and routes combined with a ground based navigational system that is about 15 years behind of where it should be. This outdated system causes congestion which means aircraft are spaced at minimums and must obey cruise assignments, even if they are capable of higher numbers. So jet aircraft travel is the fastest commercial transport, but I can't give you a speed measurement because its impossible to do so. The maximum speeds of airliners has very little to do with the cruising airspeed.