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Yes, but not on the whole stretch, not even the whole high-speed stretch (from the outskirts of Paris to Tours). Acceleration beyond 200 km/h is not so good, and moderate hills or bifurcations may cause slowdowns. The fastest Massy-St. Pierre des Corps trains cover 206.9 km in 49 minutes = 253.3 km/h on average.
We knew we were really rolling when it would start to snake, and get down to 10--which it did, occasionally, no matter what they say.
I still strongly doubt it. First, even ignoring the signalling system, going more than permitted speed +10% (that is, the top speed of type tests) would mean going into uncharted territory and thus will get you fired. But it can't come to this because there is an automated system that brakes down the train when it exceeds permitted speed by some amount, whatever the train driver does. At the top speed of 300 km/h, this is at 315 km/h, at which one kilometre is 11.4 seconds. If your trip was in the last three years, there is an outside possibility that you travelled on a train that for some reason (big lateness? special in-service trials?) had an allowed speed of 320 km/h, and superseded it to reach 335 km/h, still 10.75 seconds.
I suspect human error in clocking: a combination of differing time to look at the clock and the 1 second imprecision. At these speeds, it's better to clock times for 2-3 km.
One whose delusions are out of fashion.
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