I'm not French. French is my native language, though.

And yes, this is speculation, this is why it's a theory. There's no description of False Dragon sword, nor even much of Justice (which is 'great' and 'shiny, and that's all) in the books. All we know about Amalasan's paraphernalia is that he used what is called the 'Banner of the Light' nowadays, ie: the ancient symbol of Aes Sedai. Logain used that too. Taim adopted the Dragon itself. It's very suggestive, however, that a false Dragon might have used the serpent-with-legs had he known about it. And it's possible he did - scholars-historians know this was the sigil on LTT's banner. Moiraine, for instance, recognized it for what it was the second she saw it. Amalasan is just the most likely false Dragon, and as he fought Hawkwing, this would explain nicely why Rand finds it's a big coincidence he gets this sword now, as he is facing Hawkwing's heir.

For the rest, it's just hard to imagine anyone but a false Dragon would have used this sigil 'centuries ago'. The bit about a replica is derived from the the fact Rand specified it's odd it's him who recognized the sword, that it didn't come from LTT's memories. This implies LTT could have could have recognized the sword too, otherwise there's nothing "odd" in the fact recognition came from Rand and not him... How could LTT recognize something mere centuries old? This suggests this sword looks like another much older.