To unlock the Medieval Armor you must solve 3 puzzles in the armor room of Café Théâtre. The puzzles become available after completing Nostradamus Enigma side missions. Each side mission gives you a fragment. Use the fragments on the Nostradamus Disc in the armor room to unlock new puzzles. You must complete all 18 Nostradamus Enigmas in the game!
This will also earn you the "From the Past" trophy or achievement.
You can equip the armor in the Character Customization screen. It's listed as "Thomas de Carneillon's Master Assassin Outfit".