Brave banners and brave people draw on different branches of the same word.
Italian bravo included wild and courageous senses. Through French, brave entered English with uses including a fine or colourful show. Courage is now its familiar everyday emphasis.
Courage already existed in Italian; it did not have to develop through the English showy sense. French is omitted, and the uncertain deeper Latin proposal is excluded.
Source
Merriam-Webster: braveWord History gives Italian bravo, courageous/wild; English definitions include colourful display and courage, with the first-use record selecting showiness.