Anti-terror investigators were questioning the alleged attacker, 25-year-old Ayoub El Khazzani, who boarded the high-speed train in Brussels bound for Paris on Friday armed with a Kalashnikov assault rifle, a Luger automatic pistol, ammunition and a box-cutter.
Witnesses said he opened fire, injuring a man before being wrestled to the floor and subdued by three young Americans -- off-duty servicemen Alek Skarlatos and Spencer Stone and their student friend Anthony Sadler -- and a Briton, 62-year-old business consultant Chris Norman.
"You have shown us that, faced with terror, we have the power to resist. You have given a message of courage, solidarity and hope."
A French passenger who also tackled the gunman but chose to remain anonymous, and Eric Tanty, an off-duty train driver who happened to be on board and helped restrain Khazzani, were to be honoured too.
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Speaking as he left the Elysee, his medal pinned to his suit, Norman said it was "a little bit difficult to believe that it's actually happened".
"I think that one way or another, we are going to be facing this kind of problem quite a few times in the future, and I would invite you all to think about 'what would I do in that situation'.
"Act if the opportunity presents itself. Obviously you don't want to throw yourself in a situation that is completely hopeless, but act if you can."
Intelligence services in Belgium, France, Germany and Spain had previously flagged Khazzani as an Islamic extremist.